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Informal Introduction To Stochastic Calculus With Applications, An (Hardcover): Ovidiu Calin Informal Introduction To Stochastic Calculus With Applications, An (Hardcover)
Ovidiu Calin
R2,599 Discovery Miles 25 990 Ships in 12 - 19 working days

The goal of this book is to present Stochastic Calculus at an introductory level and not at its maximum mathematical detail. The author aims to capture as much as possible the spirit of elementary deterministic Calculus, at which students have been already exposed. This assumes a presentation that mimics similar properties of deterministic Calculus, which facilitates understanding of more complicated topics of Stochastic Calculus.

Informal Introduction To Stochastic Calculus With Applications, An (Paperback): Ovidiu Calin Informal Introduction To Stochastic Calculus With Applications, An (Paperback)
Ovidiu Calin
R1,351 Discovery Miles 13 510 Ships in 12 - 19 working days

The goal of this book is to present Stochastic Calculus at an introductory level and not at its maximum mathematical detail. The author aims to capture as much as possible the spirit of elementary deterministic Calculus, at which students have been already exposed. This assumes a presentation that mimics similar properties of deterministic Calculus, which facilitates understanding of more complicated topics of Stochastic Calculus.

Geometric Modeling in Probability and Statistics (Hardcover, 2014 ed.): Ovidiu Calin, Constantin Udriste Geometric Modeling in Probability and Statistics (Hardcover, 2014 ed.)
Ovidiu Calin, Constantin Udriste
R3,159 Discovery Miles 31 590 Ships in 12 - 19 working days

This book covers topics of Informational Geometry, a field which deals with the differential geometric study of the manifold probability density functions. This is a field that is increasingly attracting the interest of researchers from many different areas of science, including mathematics, statistics, geometry, computer science, signal processing, physics and neuroscience. It is the authors' hope that the present book will be a valuable reference for researchers and graduate students in one of the aforementioned fields. This textbook is a unified presentation of differential geometry and probability theory, and constitutes a text for a course directed at graduate or advanced undergraduate students interested in applications of differential geometry in probability and statistics. The book contains over 100 proposed exercises meant to help students deepen their understanding, and it is accompanied by software that is able to provide numerical computations of several information geometric objects. The reader will understand a flourishing field of mathematics in which very few books have been written so far.

Heat Kernels for Elliptic and Sub-elliptic Operators - Methods and Techniques (Hardcover, Edition.): Ovidiu Calin, Der-Chen... Heat Kernels for Elliptic and Sub-elliptic Operators - Methods and Techniques (Hardcover, Edition.)
Ovidiu Calin, Der-Chen Chang, Kenro Furutani, Chisato Iwasaki
R3,297 Discovery Miles 32 970 Ships in 10 - 15 working days

This monograph is a unified presentation of several theories of finding explicit formulas for heat kernels for both elliptic and sub-elliptic operators. These kernels are important in the theory of parabolic operators because they describe the distribution of heat on a given manifold as well as evolution phenomena and diffusion processes.
Heat Kernels for Elliptic and Sub-elliptic Operators is an ideal reference for graduate students, researchers in pure and applied mathematics, and theoretical physicists interested in understanding different ways of approaching evolution operators.

Geometric Mechanics on Riemannian Manifolds - Applications to Partial Differential Equations (Hardcover, 2005 ed.): Ovidiu... Geometric Mechanics on Riemannian Manifolds - Applications to Partial Differential Equations (Hardcover, 2005 ed.)
Ovidiu Calin, Der-Chen Chang
R2,752 Discovery Miles 27 520 Ships in 12 - 19 working days

* A geometric approach to problems in physics, many of which cannot be solved by any other methods

* Text is enriched with good examples and exercises at the end of every chapter

* Fine for a course or seminar directed at grad and adv. undergrad students interested in elliptic and hyperbolic differential equations, differential geometry, calculus of variations, quantum mechanics, and physics

Deterministic And Stochastic Topics In Computational Finance (Hardcover): Ovidiu Calin Deterministic And Stochastic Topics In Computational Finance (Hardcover)
Ovidiu Calin
R3,654 Discovery Miles 36 540 Ships in 12 - 19 working days

What distinguishes this book from other texts on mathematical finance is the use of both probabilistic and PDEs tools to price derivatives for both constant and stochastic volatility models, by which the reader has the advantage of computing explicitly a large number of prices for European, American and Asian derivatives.The book presents continuous time models for financial markets, starting from classical models such as Black-Scholes and evolving towards the most popular models today such as Heston and VAR.A key feature of the textbook is the large number of exercises, mostly solved, which are designed to help the reader to understand the material.The book is based on the author's lectures on topics on computational finance for senior and graduate students, delivered in USA (Princeton University and EMU), Taiwan and Kuwait. The prerequisites are an introductory course in stochastic calculus, as well as the usual calculus sequence.The book is addressed to undergraduate and graduate students in Masters of Finance programs as well as to those who wish to become more efficient in their practical applications.Topics covered:

Informal Introduction To Stochastic Calculus With Applications, An (Hardcover, Second Edition): Ovidiu Calin Informal Introduction To Stochastic Calculus With Applications, An (Hardcover, Second Edition)
Ovidiu Calin
R4,310 Discovery Miles 43 100 Ships in 10 - 15 working days

Most branches of science involving random fluctuations can be approached by Stochastic Calculus. These include, but are not limited to, signal processing, noise filtering, stochastic control, optimal stopping, electrical circuits, financial markets, molecular chemistry, population dynamics, etc. All these applications assume a strong mathematical background, which in general takes a long time to develop. Stochastic Calculus is not an easy to grasp theory, and in general, requires acquaintance with the probability, analysis and measure theory.The goal of this book is to present Stochastic Calculus at an introductory level and not at its maximum mathematical detail. The author's goal was to capture as much as possible the spirit of elementary deterministic Calculus, at which students have been already exposed. This assumes a presentation that mimics similar properties of deterministic Calculus, which facilitates understanding of more complicated topics of Stochastic Calculus.The second edition contains several new features that improved the first edition both qualitatively and quantitatively. First, two more chapters have been added, Chapter 12 and Chapter 13, dealing with applications of stochastic processes in Electrochemistry and global optimization methods.This edition contains also a final chapter material containing fully solved review problems and provides solutions, or at least valuable hints, to all proposed problems. The present edition contains a total of about 250 exercises.This edition has also improved presentation from the first edition in several chapters, including new material.

Deterministic And Stochastic Topics In Computational Finance (Paperback): Ovidiu Calin Deterministic And Stochastic Topics In Computational Finance (Paperback)
Ovidiu Calin
R1,858 Discovery Miles 18 580 Ships in 12 - 19 working days

What distinguishes this book from other texts on mathematical finance is the use of both probabilistic and PDEs tools to price derivatives for both constant and stochastic volatility models, by which the reader has the advantage of computing explicitly a large number of prices for European, American and Asian derivatives.The book presents continuous time models for financial markets, starting from classical models such as Black-Scholes and evolving towards the most popular models today such as Heston and VAR.A key feature of the textbook is the large number of exercises, mostly solved, which are designed to help the reader to understand the material.The book is based on the author's lectures on topics on computational finance for senior and graduate students, delivered in USA (Princeton University and EMU), Taiwan and Kuwait. The prerequisites are an introductory course in stochastic calculus, as well as the usual calculus sequence.The book is addressed to undergraduate and graduate students in Masters of Finance programs as well as to those who wish to become more efficient in their practical applications.Topics covered:

Deep Learning Architectures - A Mathematical Approach (Paperback, 1st ed. 2020): Ovidiu Calin Deep Learning Architectures - A Mathematical Approach (Paperback, 1st ed. 2020)
Ovidiu Calin
R2,198 Discovery Miles 21 980 Ships in 10 - 15 working days

This book describes how neural networks operate from the mathematical point of view. As a result, neural networks can be interpreted both as function universal approximators and information processors. The book bridges the gap between ideas and concepts of neural networks, which are used nowadays at an intuitive level, and the precise modern mathematical language, presenting the best practices of the former and enjoying the robustness and elegance of the latter. This book can be used in a graduate course in deep learning, with the first few parts being accessible to senior undergraduates. In addition, the book will be of wide interest to machine learning researchers who are interested in a theoretical understanding of the subject.

Sub-Riemannian Geometry - General Theory and Examples (Hardcover): Ovidiu Calin, Der-Chen Chang Sub-Riemannian Geometry - General Theory and Examples (Hardcover)
Ovidiu Calin, Der-Chen Chang
R4,065 Discovery Miles 40 650 Ships in 12 - 19 working days

Sub-Riemannian manifolds are manifolds with the Heisenberg principle built in. This comprehensive text and reference begins by introducing the theory of sub-Riemannian manifolds using a variational approach in which all properties are obtained from minimum principles, a robust method that is novel in this context. The authors then present examples and applications, showing how Heisenberg manifolds (step 2 sub-Riemannian manifolds) might in the future play a role in quantum mechanics similar to the role played by the Riemannian manifolds in classical mechanics. Sub-Riemannian Geometry: General Theory and Examples is the perfect resource for graduate students and researchers in pure and applied mathematics, theoretical physics, control theory, and thermodynamics interested in the most recent developments in sub-Riemannian geometry.

Informal Introduction To Stochastic Calculus With Applications, An (Paperback, Second Edition): Ovidiu Calin Informal Introduction To Stochastic Calculus With Applications, An (Paperback, Second Edition)
Ovidiu Calin
R2,120 Discovery Miles 21 200 Ships in 9 - 17 working days

Most branches of science involving random fluctuations can be approached by Stochastic Calculus. These include, but are not limited to, signal processing, noise filtering, stochastic control, optimal stopping, electrical circuits, financial markets, molecular chemistry, population dynamics, etc. All these applications assume a strong mathematical background, which in general takes a long time to develop. Stochastic Calculus is not an easy to grasp theory, and in general, requires acquaintance with the probability, analysis and measure theory.The goal of this book is to present Stochastic Calculus at an introductory level and not at its maximum mathematical detail. The author's goal was to capture as much as possible the spirit of elementary deterministic Calculus, at which students have been already exposed. This assumes a presentation that mimics similar properties of deterministic Calculus, which facilitates understanding of more complicated topics of Stochastic Calculus.The second edition contains several new features that improved the first edition both qualitatively and quantitatively. First, two more chapters have been added, Chapter 12 and Chapter 13, dealing with applications of stochastic processes in Electrochemistry and global optimization methods.This edition contains also a final chapter material containing fully solved review problems and provides solutions, or at least valuable hints, to all proposed problems. The present edition contains a total of about 250 exercises.This edition has also improved presentation from the first edition in several chapters, including new material.

Deep Learning Architectures - A Mathematical Approach (Hardcover, 1st ed. 2020): Ovidiu Calin Deep Learning Architectures - A Mathematical Approach (Hardcover, 1st ed. 2020)
Ovidiu Calin
R2,388 Discovery Miles 23 880 Ships in 9 - 17 working days

This book describes how neural networks operate from the mathematical point of view. As a result, neural networks can be interpreted both as function universal approximators and information processors. The book bridges the gap between ideas and concepts of neural networks, which are used nowadays at an intuitive level, and the precise modern mathematical language, presenting the best practices of the former and enjoying the robustness and elegance of the latter. This book can be used in a graduate course in deep learning, with the first few parts being accessible to senior undergraduates. In addition, the book will be of wide interest to machine learning researchers who are interested in a theoretical understanding of the subject.

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