In the last three decades, there has been a dramatic increase in the use of interacting particle methods as a powerful tool in real-world applications of Monte Carlo simulation in computational physics, population biology, computer sciences, and statistical machine learning. Ideally suited to parallel and distributed computation, these advanced particle algorithms include nonlinear interacting jump diffusions; quantum, diffusion, and resampled Monte Carlo methods; Feynman-Kac particle models; genetic and evolutionary algorithms; sequential Monte Carlo methods; adaptive and interacting Markov chain Monte Carlo models; bootstrapping methods; ensemble Kalman filters; and interacting particle filters. Mean Field Simulation for Monte Carlo Integration presents the first comprehensive and modern mathematical treatment of mean field particle simulation models and interdisciplinary research topics, including interacting jumps and McKean-Vlasov processes, sequential Monte Carlo methodologies, genetic particle algorithms, genealogical tree-based algorithms, and quantum and diffusion Monte Carlo methods. Along with covering refined convergence analysis on nonlinear Markov chain models, the author discusses applications related to parameter estimation in hidden Markov chain models, stochastic optimization, nonlinear filtering and multiple target tracking, stochastic optimization, calibration and uncertainty propagations in numerical codes, rare event simulation, financial mathematics, and free energy and quasi-invariant measures arising in computational physics and population biology. This book shows how mean field particle simulation has revolutionized the field of Monte Carlo integration and stochastic algorithms. It will help theoretical probability researchers, applied statisticians, biologists, statistical physicists, and computer scientists work better across their own disciplinary boundaries.

In the last three decades, there has been a dramatic increase in the use of interacting particle methods as a powerful tool in real-world applications of Monte Carlo simulation in computational physics, population biology, computer sciences, and statistical machine learning. Ideally suited to parallel and distributed computation, these advanced particle algorithms include nonlinear interacting jump diffusions; quantum, diffusion, and resampled Monte Carlo methods; Feynman-Kac particle models; genetic and evolutionary algorithms; sequential Monte Carlo methods; adaptive and interacting Markov chain Monte Carlo models; bootstrapping methods; ensemble Kalman filters; and interacting particle filters. Mean Field Simulation for Monte Carlo Integration presents the first comprehensive and modern mathematical treatment of mean field particle simulation models and interdisciplinary research topics, including interacting jumps and McKean-Vlasov processes, sequential Monte Carlo methodologies, genetic particle algorithms, genealogical tree-based algorithms, and quantum and diffusion Monte Carlo methods. Along with covering refined convergence analysis on nonlinear Markov chain models, the author discusses applications related to parameter estimation in hidden Markov chain models, stochastic optimization, nonlinear filtering and multiple target tracking, stochastic optimization, calibration and uncertainty propagations in numerical codes, rare event simulation, financial mathematics, and free energy and quasi-invariant measures arising in computational physics and population biology. This book shows how mean field particle simulation has revolutionized the field of Monte Carlo integration and stochastic algorithms. It will help theoretical probability researchers, applied statisticians, biologists, statistical physicists, and computer scientists work better across their own disciplinary boundaries.

This book comprises a selection of extended abstracts and papers presented at the EVOLVE 2012 held in Mexico City, Mexico. The aim of the EVOLVE is to build a bridge between probability, set oriented numerics, and evolutionary computation as to identify new common and challenging research aspects. The conference is also intended to foster a growing interest for robust and efficient methods with a sound theoretical background. EVOLVE aims to unify theory-inspired methods and cutting-edge techniques ensuring performance guarantee factors. By gathering researchers with different backgrounds, a unified view and vocabulary can emerge where the theoretical advancements may echo in different domains. Summarizing, the EVOLVE conference focuses on challenging aspects arising at the passage from theory to new paradigms and aims to provide a unified view while raising questions related to reliability, performance guarantees, and modeling. The extended papers of the EVOLVE 2012 make a contribution to this goal.

The aim of this book is to provide a strong theoretical support for understanding and analyzing the behavior of evolutionary algorithms, as well as for creating a bridge between probability, set-oriented numerics and evolutionary computation. The volume encloses a collection of contributions that were presented at the EVOLVE 2011 international workshop, held in Luxembourg, May 25-27, 2011, coming from invited speakers and also from selected regular submissions. The aim of EVOLVE is to unify the perspectives offered by probability, set oriented numerics and evolutionary computation. EVOLVE focuses on challenging aspects that arise at the passage from theory to new paradigms and practice, elaborating on the foundations of evolutionary algorithms and theory-inspired methods merged with cutting-edge techniques that ensure performance guarantee factors. EVOLVE is also intended to foster a growing interest for robust and efficient methods with a sound theoretical background. The chapters enclose challenging theoretical findings, concrete optimization problems as well as new perspectives. By gathering contributions from researchers with different backgrounds, the book is expected to set the basis for a unified view and vocabulary where theoretical advancements may echo in different domains.

This volume encloses research articles that were presented at the EVOLVE 2014 International Conference in Beijing, China, July 1 4, 2014. The book gathers contributions that emerged from the conference tracks, ranging from probability to set oriented numerics and evolutionary computation; all complemented by the bridging purpose of the conference, e.g. Complex Networks and Landscape Analysis, or by the more application oriented perspective. The novelty of the volume, when considering the EVOLVE series, comes from targeting also the practitioner s view. This is supported by the Machine Learning Applied to Networks and Practical Aspects of Evolutionary Algorithms tracks, providing surveys on new application areas, as in the networking area and useful insights in the development of evolutionary techniques, from a practitioner s perspective. Complementary to these directions, the conference tracks supporting the volume, follow on the individual advancements of the subareas constituting the scope of the conference, through the Computational Game Theory, Local Search and Optimization, Genetic Programming, Evolutionary Multi-objective optimization tracks."

Numerical methods in finance have emerged as a vital field at the crossroads of probability theory, finance and numerical analysis. Based on presentations given at the workshop Numerical Methods in Finance held at the INRIA Bordeaux (France) on June 1-2, 2010, this book provides an overview of the major new advances in the numerical treatment of instruments with American exercises. Naturally it covers the most recent research on the mathematical theory and the practical applications of optimal stopping problems as they relate to financial applications. By extension, it also provides an original treatment of Monte Carlo methods for the recursive computation of conditional expectations and solutions of BSDEs and generalized multiple optimal stopping problems and their applications to the valuation of energy derivatives and assets. The articles were carefully written in a pedagogical style and a reasonably self-contained manner. The book is geared toward quantitative analysts, probabilists, and applied mathematicians interested in financial applications.

This book comprises a selection of extended abstracts and papers presented at the EVOLVE 2012 held in Mexico City, Mexico. The aim of the EVOLVE is to build a bridge between probability, set oriented numerics, and evolutionary computation as to identify new common and challenging research aspects. The conference is also intended to foster a growing interest for robust and efficient methods with a sound theoretical background. EVOLVE aims to unify theory-inspired methods and cutting-edge techniques ensuring performance guarantee factors. By gathering researchers with different backgrounds, a unified view and vocabulary can emerge where the theoretical advancements may echo in different domains. Summarizing, the EVOLVE conference focuses on challenging aspects arising at the passage from theory to new paradigms and aims to provide a unified view while raising questions related to reliability, performance guarantees, and modeling. The extended papers of the EVOLVE 2012 make a contribution to this goal.

The aim of this book is to provide a strong theoretical support for understanding and analyzing the behavior of evolutionary algorithms, as well as for creating a bridge between probability, set-oriented numerics and evolutionary computation. The volume encloses a collection of contributions that were presented at the EVOLVE 2011 international workshop, held in Luxembourg, May 25-27, 2011, coming from invited speakers and also from selected regular submissions. The aim of EVOLVE is to unify the perspectives offered by probability, set oriented numerics and evolutionary computation. EVOLVE focuses on challenging aspects that arise at the passage from theory to new paradigms and practice, elaborating on the foundations of evolutionary algorithms and theory-inspired methods merged with cutting-edge techniques that ensure performance guarantee factors. EVOLVE is also intended to foster a growing interest for robust and efficient methods with a sound theoretical background. The chapters enclose challenging theoretical findings, concrete optimization problems as well as new perspectives. By gathering contributions from researchers with different backgrounds, the book is expected to set the basis for a unified view and vocabulary where theoretical advancements may echo in different domains.

Numerical methods in finance have emerged as a vital field at the crossroads of probability theory, finance and numerical analysis. Based on presentations given at the workshop Numerical Methods in Finance held at the INRIA Bordeaux (France) on June 1-2, 2010, this book provides an overview of the major new advances in the numerical treatment of instruments with American exercises. Naturally it covers the most recent research on the mathematical theory and the practical applications of optimal stopping problems as they relate to financial applications. By extension, it also provides an original treatment of Monte Carlo methods for the recursive computation of conditional expectations and solutions of BSDEs and generalized multiple optimal stopping problems and their applications to the valuation of energy derivatives and assets. The articles were carefully written in a pedagogical style and a reasonably self-contained manner. The book is geared toward quantitative analysts, probabilists, and applied mathematicians interested in financial applications.

This text takes readers in a clear and progressive format from simple to recent and advanced topics in pure and applied probability such as contraction and annealed properties of non-linear semi-groups, functional entropy inequalities, empirical process convergence, increasing propagations of chaos, central limit, and Berry Esseen type theorems as well as large deviation principles for strong topologies on path-distribution spaces. Topics also include a body of powerful branching and interacting particle methods.

This text takes readers in a clear and progressive format from simple to recent and advanced topics in pure and applied probability such as contraction and annealed properties of non-linear semi-groups, functional entropy inequalities, empirical process convergence, increasing propagations of chaos, central limit, and Berry Esseen type theorems as well as large deviation principles for strong topologies on path-distribution spaces. Topics also include a body of powerful branching and interacting particle methods.

This book comprises a selection of papers from the EVOLVE 2012 held in Mexico City, Mexico. The aim of the EVOLVE is to build a bridge between probability, set oriented numerics and evolutionary computing, as to identify new common and challenging research aspects. The conference is also intended to foster a growing interest for robust and efficient methods with a sound theoretical background. EVOLVE is intended to unify theory-inspired methods and cutting-edge techniques ensuring performance guarantee factors. By gathering researchers with different backgrounds, a unified view and vocabulary can emerge where the theoretical advancements may echo in different domains. Summarizing, the EVOLVE focuses on challenging aspects arising at the passage from theory to new paradigms and aims to provide a unified view while raising questions related to reliability, performance guarantees and modeling. The papers of the EVOLVE 2012 make a contribution to this goal.

La theorie des probabilites et des processus stochastiques est sans aucun doute l'un des plus importants outils mathematiques des sciences modernes. Le theorie des probabilite s'illustre dans de nombreux domaines issus de la biologie, de la physique, et des sciences de l'ingenieur: dynamique des populations, traitement du signal et de l'image, chimie moleculaire, econometrie, sciences actuarielles, mathematiques financieres, ainsi qu'en analyse de risque. Le but de cet ouvrage est de parcourir les principaux modeles et methodes stochastiques de cette theorie en pleine expansion. Ce voyage ne necessite aucun bagage specifique sur la theorie des processus stochastiques. Les outils d'analyses necessaires a une bonne comprehension sont donnes au fur et a mesure de leur construction, revelant ainsi leur necessite. La theorie des processus stochastiques est une extension naturelle de la theorie de systemes dynamiques a des phenomenes aleatoires. Elle contient des formalisation d'evolutions de phenomenes aleatoires rencontres en physique, en biologique, en economie, ou en sciences de l'ingenieur, mais aussi des algorithmes d'exploration stochastique d'espaces de solutions complexes pour resoudre des problemes d'estimation, d'optimisation et d'apprentissage statistique. Des techniques de resolution avancees en statistique bayesienne, en traitement du signal, en analyse d'evenements rares, en combinatoire enumerative, en optimisation combinatoire, ainsi qu'en physique et chimie quantique sont exposees dans cet ouvrage.

Probability theory and stochastic process theory are undoubtedly among the most important mathematic tools for the modern sciences. Probability theory has applications in several fields, such as biology, physics and the engineering sciences: population dynamics, signal and image processing, molecular chemistry, econometrics, actuarial science, financial mathematics, and risk analysis. This book provides an overview of stochastic models and methods for this very active field. Stochastic process theory is a natural extension of dynamic systems to random events. The book covers the modeling of random events in physics, biology, economics and the engineering sciences, while also introducing advanced problem-solving techniques in Bayesian statistics, signal processing and rare event analysis. No scientific background in stochastic process theory is needed."

This book presents some new concentration inequalities for Feynman-Kac particle processes. It analyzes different types of stochastic particle models, including particle profile occupation measures, genealogical tree based evolution models, particle free energies, as well as backward Markov chain particle models. It illustrates these results with a series of topics related to computational physics and biology, stochastic optimization, signal processing and Bayesian statistics, and many other probabilistic machine learning algorithms. Special emphasis is given to the stochastic modeling, and to the quantitative performance analysis of a series of advanced Monte Carlo methods; including particle filters, genetic type island models, Markov bridge models, and interacting particle Markov chain Monte Carlo methodologies.

Random matrix theory plays a central role in statistical physics, computational mathematics and engineering sciences, including data assimilation, signal processing, combinatorial optimization, compressed sensing, econometrics and mathematical finance, among numerous others. The mathematical foundations of the theory of random matrices are technical, and mathematically difficult to penetrate for non-experts, regular users and practitioners. This book reviews and extends some important results in random matrix theory in the specific context of real random Wishart matrices. To overcome the complexity of the subject matter, the authors use a lecture note style to make the material accessible to a wide audience. This results in a comprehensive and self-contained introduction to the analysis of Wishart matrix moments. This study may act as an introduction to some particular aspects of random matrix theory, or as a self-contained exposition of Wishart matrix moments. All researchers and students requiring an accessible introduction to the topic will find this book essential reading.