Probability Theory And Stochastic Processes

Authors: Bouleau, Nicolas, Denis, Laurent
Presents a new approach to absolute continuity and regularity of laws of Poisson functionals
Richly illustrated by various examples
​Introduces a new mathematical tool, the "lent particle method

Authors: Čekanavičius, Vydas
Presents a unique collection of approximation methods in various metrics
Explains the essential aspects of each method in detail
Includes many exercises with solutions as well as bibliographical notes

The purpose of this book is twofold: first, it sets out to equip the reader with a sound understanding of the foundations of probability theory and stochastic processes, offering step-by-step guidance from basic probability theory to advanced topics, such as stochastic differential equations, which typically are presented in textbooks that require a very strong mathematical background. Second, while leading the reader on this journey, it aims to impart the knowledge needed in order to develop algorithms that simulate realistic physical systems.

by Aurélien Alfonsi (Author)

Preface In the axioms of probability theory proposed by Kolmogorov the basic "probabilistic" object is the concept of a probability model or probability space. This is a triple (n, F, P), where n is the space of elementary events or outcomes, F is a a-algebra of subsets of n announced by the events and P is a probability measure or a probability on the measure space (n, F). This generally accepted system of axioms of probability theory proved to be so successful that, apart from its simplicity, it enabled one to embrace the classical branches of probability theory and, at the same time, it paved the way for the development of new chapters in it, in particular, the theory of random (or stochastic) processes. In the theory of random processes, various classes of processes have been studied in depth.