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Markov Processes, Brownian Motion, and Time Symmetry
The book consists of two parts. Part I,This part introduces strong Markov processes and their potential theory. In particular,it studies Brownian motion, and shows how it generates classical potential theory.Part II, focus on the effects of time reversal, duality, and time-symmetry on potential theory. Certain theorems in Part I are re-proved in Part II under slightly weaker hypotheses. The volume is very useful for people who wish to learn Markov processes but it seems to the reviewer that it is also of great interest to specialists in this area who could derive much stimulus from it. One can be convinced that it will receive wide circulation." (Mathematical Reviews)
Applied Semi-Markov Processes
The book presents homogeneous and non-homogeneous semi-Markov processes, as well as Markov and semi-Markov rewards processes. These concepts are fundamental for many applications, but they are not as thoroughly presented in other books on the subject as they are here.This book is intended for graduate students and researchers in mathematics, operations research and engineering; it might also appeal to actuaries and financial managers, and anyone interested in its applications for banks, mechanical industries for reliability aspects, and insurance companies.
An Introduction to Markov Processes
Provides a more accessible introduction than other books on Markov processes by emphasizing the structure of the subject and avoiding sophisticated measure theoryLeads the reader to a rigorous understanding of basic theory
An Introduction to Infinite-Dimensional Analysis
In this revised and extended version of his course notes from a 1-year course at Scuola Normale Superiore, Pisa, the author provides an introduction – for an audience knowing basic functional analysis and measure theory but not necessarily probability theory – to analysis in a separable Hilbert space of infinite dimension.Starting from the definition of Gaussian measures in Hilbert spaces, concepts such as the Cameron-Martin formula, Brownian motion and Wiener integral are introduced in a simple way. These concepts are then used to illustrate some basic stochastic dynamical systems (including dissipative nonlinearities) and Markov semi-groups, paying special attention to their long-time behavior: ergodicity, invariant measure. Here fundamental results like the theorems of Prokhorov, Von Neumann, Krylov-Bogoliubov and Khas'minski are proved. The last chapter is devoted to gradient systems and their asymptotic behavior.
