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Books > Science & Mathematics > Mathematics > Applied mathematics > Stochastics

Markov Processes from K. Ito's Perspective (AM-155) (Paperback): Daniel W. Stroock Markov Processes from K. Ito's Perspective (AM-155) (Paperback)
Daniel W. Stroock
R1,900 Discovery Miles 19 000 Ships in 12 - 17 working days

Kiyosi Ito's greatest contribution to probability theory may be his introduction of stochastic differential equations to explain the Kolmogorov-Feller theory of Markov processes. Starting with the geometric ideas that guided him, this book gives an account of Ito's program.

The modern theory of Markov processes was initiated by A. N. Kolmogorov. However, Kolmogorov's approach was too analytic to reveal the probabilistic foundations on which it rests. In particular, it hides the central role played by the simplest Markov processes: those with independent, identically distributed increments. To remedy this defect, Ito interpreted Kolmogorov's famous forward equation as an equation that describes the integral curve of a vector field on the space of probability measures. Thus, in order to show how Ito's thinking leads to his theory of stochastic integral equations, Stroock begins with an account of integral curves on the space of probability measures and then arrives at stochastic integral equations when he moves to a pathspace setting. In the first half of the book, everything is done in the context of general independent increment processes and without explicit use of Ito's stochastic integral calculus. In the second half, the author provides a systematic development of Ito's theory of stochastic integration: first for Brownian motion and then for continuous martingales. The final chapter presents Stratonovich's variation on Ito's theme and ends with an application to the characterization of the paths on which a diffusion is supported.

The book should be accessible to readers who have mastered the essentials of modern probability theory and should provide such readers with a reasonably thorough introduction to continuous-time, stochastic processes."

Seminaire de Probabilites 1967-1980 - A Selection in Martingale Theory (French, English, Paperback, 2002 ed.): Michel Emery,... Seminaire de Probabilites 1967-1980 - A Selection in Martingale Theory (French, English, Paperback, 2002 ed.)
Michel Emery, Marc Yor
R1,770 Discovery Miles 17 700 Ships in 10 - 15 working days

Twenty-five articles have been selected from the first 14 volumes of the "SA(c)minaire de ProbabilitA(c)s," all out of print, for their historical and/or mathematical interest. Among the many articles devoted to Martingale theory in the early volumes of the SA(c)minaire, we have chosen to reprint those that are particularly significant from a historical point of view, as well as those that can still be useful today. They are reprinted here verbatim, with a short retrospective comment, for the benefit of researchers in the theory of stochastic processes, in mathematical finance, or in history of mathematics.

Diffusions, Markov Processes And Martingales - Volume 2 - Ito Calculus (Paperback, 2nd Revised edition): L. C. G. Rogers, David... Diffusions, Markov Processes And Martingales - Volume 2 - Ito Calculus (Paperback, 2nd Revised edition)
L. C. G. Rogers, David Williams
R2,099 Discovery Miles 20 990 Ships in 12 - 17 working days

The second volume concentrates on stochastic integrals, stochastic differential equations, excursion theory and the general theory of processes. These subjects are made accessible in the many concrete examples that illustrate techniques of calculation, and in the treatment of all topics from the ground up, starting from simple cases. Many of the examples and proofs are new; some important calculational techniques appear for the first time in this book.

Derivatives in Financial Markets with Stochastic Volatility (Hardcover): Jean-Pierre Fouque, George Papanicolaou, K. Ronnie... Derivatives in Financial Markets with Stochastic Volatility (Hardcover)
Jean-Pierre Fouque, George Papanicolaou, K. Ronnie Sircar
R2,900 Discovery Miles 29 000 Ships in 12 - 17 working days

This important work addresses problems in financial mathematics of pricing and hedging derivative securities in an environment of uncertain and changing market volatility. These problems are important to investors from large trading institutions to pension funds. The authors present mathematical and statistical tools that exploit the volatile nature of the market. The mathematics is introduced through examples and illustrated with simulations and the modeling approach that is described is validated and tested on market data. The material is suitable for a one-semester course for graduate students with some exposure to methods of stochastic modeling and arbitrage pricing theory in finance. The volume is easily accessible to derivatives practitioners in the financial engineering industry.

Diffusions, Markov Processes, and Martingales: Volume 1, Foundations (Paperback, 2nd Revised edition): L. C. G. Rogers, David... Diffusions, Markov Processes, and Martingales: Volume 1, Foundations (Paperback, 2nd Revised edition)
L. C. G. Rogers, David Williams
R2,055 Discovery Miles 20 550 Ships in 12 - 17 working days

Now available in paperback, this celebrated book remains a key systematic guide to a large part of the modern theory of Probability. The authors not only present the subject of Brownian motion as a dry part of mathematical analysis, but convey its real meaning and fascination. The opening, heuristic chapter does just this, and it is followed by a comprehensive and self-contained account of the foundations of theory of stochastic processes. Chapter 3 is a lively presentation of the theory of Markov processes. Together with its companion volume, this book equips graduate students for research into a subject of great intrinsic interest and wide applications.

Seminaire de Probabilites XXXII (French, English, Paperback, 1998 ed.): Jacques Azema, Michel Emery, Michel Ledoux, Marc Yor Seminaire de Probabilites XXXII (French, English, Paperback, 1998 ed.)
Jacques Azema, Michel Emery, Michel Ledoux, Marc Yor
R1,702 Discovery Miles 17 020 Ships in 10 - 15 working days

All the papers in the volume are original research papers, discussing fundamental properties of stochastic processes. The topics under study (martingales, filtrations, path properties, etc.) represent an important part of the current research performed in 1996-97 by various groups of probabilists in France and abroad.

Symbolic Dynamics - One-sided, Two-sided and Countable State Markov Shifts (Paperback, Softcover reprint of the original 1st... Symbolic Dynamics - One-sided, Two-sided and Countable State Markov Shifts (Paperback, Softcover reprint of the original 1st ed. 1998)
Bruce P. Kitchens
R2,703 Discovery Miles 27 030 Ships in 10 - 15 working days

Nearly one hundred years ago Jacques Hadamard used infinite sequences of symbols to analyze the distribution of geodesics on certain surfaces. That was the beginning of symbolic dynamics. In the 1930's and 40's Arnold Hedlund and Marston Morse again used infinite sequences to investigate geodesics on surfaces of negative curvature. They coined the term symbolic dynamics and began to study sequence spaces with the shift transformation as dynamical systems. In the 1940's Claude Shannon used sequence spaces to describe infor mation channels. Since that time symbolic dynamics has been used in ergodic theory, topological dynamics, hyperbolic dynamics, information theory and complex dynamics. Symbolic dynamical systems with a finite memory are stud ied in this book. They are the topological Markov shifts. Each can be defined by transition rules and the rules can be summarized by a transition matrix. The study naturally divides into two parts. The first part is about topological Markov shifts where the alphabet is finite. The second part is concerned with topological Markov shifts whose alphabet is count ably infinite. The techniques used in the two cases are quite different. When the alphabet is finite most of the methods are combinatorial or algebraic. When the alphabet is infinite the methods are much more analytic. This book grew from notes for a graduate course taught at Wesleyan Uni versity in the fall of 1994 and is intended as a graduate text and as a reference book for mathematicians working in related fields."

Meromorphic Dynamics 2 Volume Hardback Set (Hardcover): Janina Kotus, Mariusz Urbanski Meromorphic Dynamics 2 Volume Hardback Set (Hardcover)
Janina Kotus, Mariusz Urbanski
R5,641 Discovery Miles 56 410 Ships in 12 - 17 working days

This two-volume set provides a comprehensive and self-contained approach to the dynamics, ergodic theory, and geometry of elliptic functions mapping the complex plane onto the Riemann sphere. Volume I discusses many fundamental results from ergodic theory and geometric measure theory in detail, including finite and infinite abstract ergodic theory, Young's towers, measure-theoretic Kolmogorov-Sinai entropy, thermodynamics formalism, geometric function theory, various conformal measures, conformal graph directed Markov systems and iterated functions systems, classical theory of elliptic functions. In Volume II, all these techniques, along with an introduction to topological dynamics of transcendental meromorphic functions, are applied to describe the beautiful and rich dynamics and fractal geometry of elliptic functions. Much of this material is appearing for the first time in book or even paper form. Both researchers and graduate students will appreciate the detailed explanations of essential concepts and full proofs provided in what is sure to be an indispensable reference.

Stochastic Modeling for Medical Image Analysis (Hardcover): Ayman El-Baz, Georgy Gimel'farb, Jasjit S. Suri Stochastic Modeling for Medical Image Analysis (Hardcover)
Ayman El-Baz, Georgy Gimel'farb, Jasjit S. Suri
R5,604 Discovery Miles 56 040 Ships in 12 - 17 working days

Stochastic Modeling for Medical Image Analysis provides a brief introduction to medical imaging, stochastic modeling, and model-guided image analysis. Today, image-guided computer-assisted diagnostics (CAD) faces two basic challenging problems. The first is the computationally feasible and accurate modeling of images from different modalities to obtain clinically useful information. The second is the accurate and fast inferring of meaningful and clinically valid CAD decisions and/or predictions on the basis of model-guided image analysis. To help address this, this book details original stochastic appearance and shape models with computationally feasible and efficient learning techniques for improving the performance of object detection, segmentation, alignment, and analysis in a number of important CAD applications. The book demonstrates accurate descriptions of visual appearances and shapes of the goal objects and their background to help solve a number of important and challenging CAD problems. The models focus on the first-order marginals of pixel/voxel-wise signals and second- or higher-order Markov-Gibbs random fields of these signals and/or labels of regions supporting the goal objects in the lattice. This valuable resource presents the latest state of the art in stochastic modeling for medical image analysis while incorporating fully tested experimental results throughout.

Discrete Stochastic Processes and Optimal Filtering (Hardcover): JC Bertein Discrete Stochastic Processes and Optimal Filtering (Hardcover)
JC Bertein
R4,218 Discovery Miles 42 180 Ships in 12 - 17 working days

Optimal filtering applied to stationary and non-stationary signals provides the most efficient means of dealing with problems arising from the extraction of noise signals. Moreover, it is a fundamental feature in a range of applications, such as in navigation in aerospace and aeronautics, filter processing in the telecommunications industry, etc. This book provides a comprehensive overview of this area, discussing random and Gaussian vectors, outlining the results necessary for the creation of Wiener and adaptive filters used for stationary signals, as well as examining Kalman filters which are used in relation to non-stationary signals. Exercises with solutions feature in each chapter to demonstrate the practical application of these ideas using Matlab.

Seminaire de Probabilites XXIV 1988/89 (French, English, Paperback, 1990 ed.): Jacques Azema, Paul A. Meyer, Marc Yor Seminaire de Probabilites XXIV 1988/89 (French, English, Paperback, 1990 ed.)
Jacques Azema, Paul A. Meyer, Marc Yor
R1,834 Discovery Miles 18 340 Ships in 10 - 15 working days

The different papers contained in this volume are all research papers. The main directions of research which are being developed are: quantum probability, semimartingales and stochastic calculus.

Markov Chains - From Theory to Implementation and Experimentation (Hardcover): PA Gagniuc Markov Chains - From Theory to Implementation and Experimentation (Hardcover)
PA Gagniuc
R2,903 Discovery Miles 29 030 Ships in 12 - 17 working days

A fascinating and instructive guide to Markov chains for experienced users and newcomers alike This unique guide to Markov chains approaches the subject along the four convergent lines of mathematics, implementation, simulation, and experimentation. It introduces readers to the art of stochastic modeling, shows how to design computer implementations, and provides extensive worked examples with case studies. Markov Chains: From Theory to Implementation and Experimentation begins with a general introduction to the history of probability theory in which the author uses quantifiable examples to illustrate how probability theory arrived at the concept of discrete-time and the Markov model from experiments involving independent variables. An introduction to simple stochastic matrices and transition probabilities is followed by a simulation of a two-state Markov chain. The notion of steady state is explored in connection with the long-run distribution behavior of the Markov chain. Predictions based on Markov chains with more than two states are examined, followed by a discussion of the notion of absorbing Markov chains. Also covered in detail are topics relating to the average time spent in a state, various chain configurations, and n-state Markov chain simulations used for verifying experiments involving various diagram configurations. Fascinating historical notes shed light on the key ideas that led to the development of the Markov model and its variants Various configurations of Markov Chains and their limitations are explored at length Numerous examples from basic to complex are presented in a comparative manner using a variety of color graphics All algorithms presented can be analyzed in either Visual Basic, Java Script, or PHP Designed to be useful to professional statisticians as well as readers without extensive knowledge of probability theory Covering both the theory underlying the Markov model and an array of Markov chain implementations, within a common conceptual framework, Markov Chains: From Theory to Implementation and Experimentation is a stimulating introduction to and a valuable reference for those wishing to deepen their understanding of this extremely valuable statistical tool. Paul A. Gagniuc, PhD, is Associate Professor at Polytechnic University of Bucharest, Romania. He obtained his MS and his PhD in genetics at the University of Bucharest. Dr. Ganiuc s work has been published in numerous high profile scientific journals, ranging from the Public Library of Science to BioMed Central and Nature journals. He is the recipient of several awards for exceptional scientific results and a highly active figure in the review process for different scientific areas.

Anwendungen Der Potentialtheorie Auf Geophysikalische Felder (German, Paperback, Softcover Reprint of the Original 1st 1986... Anwendungen Der Potentialtheorie Auf Geophysikalische Felder (German, Paperback, Softcover Reprint of the Original 1st 1986 ed.)
Rolf Gutdeutsch
R1,869 Discovery Miles 18 690 Ships in 10 - 15 working days
Sminaire de Theorie Du Potentiel Paris, No. 7 (French, Paperback, 1984 ed.): M. Brelot Sminaire de Theorie Du Potentiel Paris, No. 7 (French, Paperback, 1984 ed.)
M. Brelot; Contributions by F. Hirsch; Directed by G. Choquet; Contributions by G Mokobodzki; Directed by J. Deny
R1,292 Discovery Miles 12 920 Ships in 10 - 15 working days
Seminaire de Theorie Du Potentiel, Paris, No. 6 (French, Paperback, 1982 ed.): M. Brelot Seminaire de Theorie Du Potentiel, Paris, No. 6 (French, Paperback, 1982 ed.)
M. Brelot; Contributions by F. Hirsch; Directed by G. Choquet; Contributions by G Mokobodzki; Directed by J. Deny
R1,304 Discovery Miles 13 040 Ships in 10 - 15 working days
Spectral Expansion of the Transfer Matrices of Gibbs Fields (Paperback, 2nd ed.): Robert A. Minlos Spectral Expansion of the Transfer Matrices of Gibbs Fields (Paperback, 2nd ed.)
Robert A. Minlos
R1,138 Discovery Miles 11 380 Ships in 10 - 15 working days
Seminar UEber Potentialtheorie (German, Paperback, 1968 ed.): Heinz Bauer Seminar UEber Potentialtheorie (German, Paperback, 1968 ed.)
Heinz Bauer
R870 Discovery Miles 8 700 Ships in 10 - 15 working days
Limit Distributions for Sums of Independent Random Variables (Paperback): B.V. Gnedenko, A.N. Kolmogorov Limit Distributions for Sums of Independent Random Variables (Paperback)
B.V. Gnedenko, A.N. Kolmogorov; Translated by K.L. Chung
R578 Discovery Miles 5 780 Ships in 10 - 15 working days
Probability Theory (Paperback): S. R. S. Varadhan Probability Theory (Paperback)
S. R. S. Varadhan
R854 Discovery Miles 8 540 Ships in 12 - 17 working days

This volume presents topics in probability theory covered during a first-year graduate course given at the Courant Institute of Mathematical Sciences, USA. The necessary background material in measure theory is developed, including the standard topics, such as extension theorem, construction of measures, integration, product spaces, Radon-Nikodym theorem, and conditional expectation In the first part of the book, characteristic functions are introduced, followed by the study of weak convergence of probability distributions. Then both the weak and strong limit theorems for sums of independent random variables are proved, including the weak and strong laws of large numbers, central limit theorems, laws of the iterated logarithm, and the Kolmogorov three series theorem. The first part concludes with infinitely divisible distributions and limit theorems for sums of uniformly infinitesimal independent random variables. The second part of the book mainly deals with dependent random variables, particularly martingales and Markov chains. Topics include standard results regarding discrete parameter martingales and Doob's inequalities.

Basics and Trends in Sensitivity Analysis - Theory and Practice in R (Paperback): Sebastien Da Veiga, Fabrice Gamboa, Bertrand... Basics and Trends in Sensitivity Analysis - Theory and Practice in R (Paperback)
Sebastien Da Veiga, Fabrice Gamboa, Bertrand Iooss, Clementine Prieur
R2,511 R2,190 Discovery Miles 21 900 Save R321 (13%) Ships in 12 - 17 working days

This book provides an overview of global sensitivity analysis methods and algorithms, including their theoretical basis and mathematical properties. The authors use a practical point of view and real case studies as well as numerous examples, and applications of the different approaches are illustrated throughout using R code to explain their usage and usefulness in practice. Basics and Trends in Sensitivity Analysis: Theory and Practice in R covers a lot of material, including theoretical aspects of Sobol' indices as well as sampling-based formulas, spectral methods, and metamodel-based approaches for estimation purposes; screening techniques devoted to identifying influential and noninfluential inputs; variance-based measures when model inputs are statistically dependent (and several other approaches that go beyond variance-based sensitivity measures); and a case study in R related to a COVID-19 epidemic model where the full workflow of sensitivity analysis combining several techniques is presented. This book is intended for engineers, researchers, and undergraduate students who use complex numerical models and have an interest in sensitivity analysis techniques and is appropriate for anyone with a solid mathematical background in basic statistical and probability theories who develops and uses numerical models in all scientific and engineering domains.

Cracking the Finance Quant Interview - 75 Interview Questions and Solutions (Paperback): Editions Ducourt Cracking the Finance Quant Interview - 75 Interview Questions and Solutions (Paperback)
Editions Ducourt; Jean Peyre
R461 Discovery Miles 4 610 Ships in 10 - 15 working days
Reliability Calculations with the Stochastic Finite Element (Paperback): Wenhui Mo Reliability Calculations with the Stochastic Finite Element (Paperback)
Wenhui Mo
R1,348 Discovery Miles 13 480 Ships in 10 - 15 working days
A First Course in Stochastic Models (Hardcover, 2 Rev Ed): H. C. Tijms A First Course in Stochastic Models (Hardcover, 2 Rev Ed)
H. C. Tijms
R1,610 Discovery Miles 16 100 Ships in 12 - 17 working days

The field of applied probability has changed profoundly in the past twenty years. The development of computational methods has greatly contributed to a better understanding of the theory. A First Course in Stochastic Models provides a self-contained introduction to the theory and applications of stochastic models. Emphasis is placed on establishing the theoretical foundations of the subject, thereby providing a framework in which the applications can be understood. Without this solid basis in theory no applications can be solved.

  • Provides an introduction to the use of stochastic models through an integrated presentation of theory, algorithms and applications.

  • Incorporates recent developments in computational probability.

  • Includes a wide range of examples that illustrate the models and make the methods of solution clear.

  • Features an abundance of motivating exercises that help the student learn how to apply the theory.

  • Accessible to anyone with a basic knowledge of probability.
A First Course in Stochastic Models is suitable for senior undergraduate and graduate students from computer science, engineering, statistics, operations research, and any other discipline where stochastic modelling takes place. It stands out amongst other textbooks on the subject because of its integrated presentation of theory, algorithms and applications.
Introduction to the Numerical Solution of Markov Chains (Hardcover, New): William J. Stewart Introduction to the Numerical Solution of Markov Chains (Hardcover, New)
William J. Stewart
R3,399 R3,179 Discovery Miles 31 790 Save R220 (6%) Ships in 12 - 17 working days

A cornerstone of applied probability, Markov chains can be used to help model how plants grow, chemicals react, and atoms diffuse--and applications are increasingly being found in such areas as engineering, computer science, economics, and education. To apply the techniques to real problems, however, it is necessary to understand how Markov chains can be solved numerically. In this book, the first to offer a systematic and detailed treatment of the numerical solution of Markov chains, William Stewart provides scientists on many levels with the power to put this theory to use in the actual world, where it has applications in areas as diverse as engineering, economics, and education. His efforts make for essential reading in a rapidly growing field.

Here Stewart explores all aspects of numerically computing solutions of Markov chains, especially when the state is huge. He provides extensive background to both discrete-time and continuous-time Markov chains and examines many different numerical computing methods--direct, single-and multi-vector iterative, and projection methods. More specifically, he considers recursive methods often used when the structure of the Markov chain is upper Hessenberg, iterative aggregation/disaggregation methods that are particularly appropriate when it is NCD (nearly completely decomposable), and reduced schemes for cases in which the chain is periodic. There are chapters on methods for computing transient solutions, on stochastic automata networks, and, finally, on currently available software. Throughout Stewart draws on numerous examples and comparisons among the methods he so thoroughly explains.

Stochastik 2 - Von der Standardabweichung bis zur Beurteilenden Statistik (German, Paperback, 1. Aufl. 2020): Michael Barot,... Stochastik 2 - Von der Standardabweichung bis zur Beurteilenden Statistik (German, Paperback, 1. Aufl. 2020)
Michael Barot, Juraj Hromkovic
R884 R615 Discovery Miles 6 150 Save R269 (30%) Ships in 12 - 17 working days

Aufbauend auf dem ersten Band, werden in diesem Buch weiterfuhrende Konzepte der Wahrscheinlichkeitstheorie ausfuhrlich und verstandlich diskutiert. Mit vielen exemplarisch durchgerechneten Aufgaben, einer Vielzahl weiterer Problemstellungen und ausfuhrlichen Loesungen bietet es dem Leser die Moeglichkeit, die eigenen Fahigkeiten standig zu erweitern und kritisch zu uberprufen und ein tieferes Verstandnis der Materie zu erlangen. Realitatsnahe Anwendungen ermoeglichen einen Ausblick in die breite Verwendbarkeit dieser Theorie.Auch in diesem Band wird auf die Entwicklung der Begriffsbildung und der mathematischen Konzepte besonderer Wert gelegt, sodass man ihre Bedeutung bei der Erzeugung wie auch standige Verbesserung von Forschungsinstrumenten fur die Untersuchung unserer Welt erleben kann. Gerichtet ist das Buch an Gymnasiasten, Studienanfanger an Hochschulen, Lehrer und Interessierte, die sich mit diesem Gebiet vertraut machen moechten.

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