TY - BOOK ID - 78640557 TI - Stochastic analysis and diffusion processes AU - Kallianpur, Gopinath AU - Sundar, P. PY - 2014 VL - 24 SN - 0191631442 9780191631443 0199657068 9780199657063 9780191781759 0191781754 0199657076 9780199657070 0199657068 9780199657063 0191004529 PB - Oxford : Oxford University Press, DB - UniCat KW - Stochastic analysis. KW - Markov processes. KW - Analysis, Markov KW - Chains, Markov KW - Markoff processes KW - Markov analysis KW - Markov chains KW - Markov models KW - Models, Markov KW - Processes, Markov KW - Stochastic processes KW - Analysis, Stochastic KW - Mathematical analysis KW - Diffusion processes. UR - https://www.unicat.be/uniCat?func=search&query=sysid:78640557 AB - "Stochastic Analysis and Diffusion Processes presents a simple, mathematical introduction to Stochastic Calculus and its applications. The book builds the basic theory and offers a careful account of important research directions in Stochastic Analysis. The breadth and power of Stochastic Analysis, and probabilistic behavior of diffusion processes are told without compromising on the mathematical details. Starting with the construction of stochastic processes, the book introduces Brownian motion and martingales. The book proceeds to construct stochastic integrals, establish the Itô formula, and discuss its applications. Next, attention is focused on stochastic differential equations (SDEs) which arise in modeling physical phenomena, perturbed by random forces. Diffusion processes are solutions of SDEs and form the main theme of this book. The Stroock-Varadhan martingale problem, the connection between diffusion processes and partial differential equations, Gaussian solutions of SDEs, and Markov processes with jumps are presented in successive chapters. The book culminates with a careful treatment of important research topics such as invariant measures, ergodic behavior, and large deviation principle for diffusions. Examples are given throughout the book to illustrate concepts and results. In addition, exercises are given at the end of each chapter that will help the reader to understand the concepts better. The book is written for graduate students, young researchers and applied scientists who are interested in stochastic processes and their applications. The reader is assumed to be familiar with probability theory at graduate level. The book can be used as a text for a graduate course on Stochastic Analysis." -- Provided by publisher. ER -