Probability theory on compact Lie groups deals with the interaction between “chance” and “symmetry,” a beautiful area of mathematics of great interest in its own sake but which is now also finding increasing applications in statistics and engineering (particularly with respect to signal processing).  Meer

The focus of the present volume is stochastic optimization of dynamical systems in discrete time where - by concentrating on the role of information regarding optimization problems - it discusses the related discretization issues.  Meer

The authors present a concise but complete exposition of the mathematical theory of stable convergence and give various applications in different areas of probability theory and mathematical statistics to illustrate the usefulness of this concept.  Meer

Considering Poisson random measures as the driving sources for stochastic (partial) differential equations allows us to incorporate jumps and to model sudden, unexpected phenomena.  Meer

This monograph, now in a thoroughly revised second edition, develops the theory of stochastic calculus in Hilbert spaces and applies the results to the study of generalized solutions of stochastic parabolic equations.  Meer

This book provides an introduction to the theory and applications of point processes, both in time and in space. Presenting the two components of point process calculus, the martingale calculus and the Palm calculus, it aims to develop the computational skills needed for the study of stochastic models involving point processes, providing enough of the general theory for the reader to reach a technical level sufficient for most applications.  Meer

This book provides an introduction to the theory and applications of point processes, both in time and in space. Presenting the two components of point process calculus, the martingale calculus and the Palm calculus, it aims to develop the computational skills needed for the study of stochastic models involving point processes, providing enough of the general theory for the reader to reach a technical level sufficient for most applications.  Meer

This new, thoroughly revised and expanded 3rd edition of a classic gives a comprehensive coverage of modern probability in a single book. It is a truly modern text, providing not only classical results but also material that will be important for future research.  Meer

The first edition of this single volume on the theory of probability has become a highly-praised standard reference for many areas of probability theory.  Meer

This book is aimed at researchers, graduate students and engineers who would like to be initiated to Piecewise Deterministic Markov Processes (PDMPs).  Meer

This book presents fundamental relations between random walks on graphs and field theories of mathematical physics. Such relations have been explored for several decades and remain a rapidly developing research area in probability theory.  Meer

This monograph, now in a thoroughly revised second edition, offers the latest research on random sets. It has been extended to include substantial developments achieved since 2005, some of them motivated by applications of random sets to econometrics and finance.  Meer

This book presents broadly applicable methods for the large deviation and moderate deviation analysis of discrete and continuous time stochastic systems.  Meer

This book undertakes a detailed construction of Dynamic Markov Bridges using a combination of theory and real-world applications to drive home important concepts and methodologies.  Meer

This book provides a systematic and accessible approach to stochastic differential equations, backward stochastic differential equations, and their connection with partial differential equations, as well as the recent development of the fully nonlinear theory, including nonlinear expectation, second order backward stochastic differential equations, and path dependent partial differential equations.  Meer

This sequel to Brownian Motion and Stochastic Calculus by the same authors develops contingent claim pricing and optimal consumption/investment in both complete and incomplete markets, within the context of Brownian-motion-driven asset prices.  Meer

This book contains an in-depth treatment of matrix-exponential (ME) distributions and their sub-class of phase-type (PH) distributions. Loosely speaking, an ME distribution  is obtained through replacing the intensity parameter in an exponential distribution by a matrix.  Meer

This book contains an in-depth treatment of matrix-exponential (ME) distributions and their sub-class of phase-type (PH) distributions. Loosely speaking, an ME distribution  is obtained through replacing the intensity parameter in an exponential distribution by a matrix.  Meer

This book provides a systematic and accessible approach to stochastic differential equations, backward stochastic differential equations, and their connection with partial differential equations, as well as the recent development of the fully nonlinear theory, including nonlinear expectation, second order backward stochastic differential equations, and path dependent partial differential equations.  Meer

Ces notes sont consacrées aux inégalités et aux théorèmes limites classiques pour les suites de variables aléatoires absolument régulières ou fortement mélangeantes au sens de Rosenblatt.  Meer