Notice bibliographique
- Notice
Type(s) de contenu et mode(s) de consultation : Texte noté : sans médiation
Auteur(s) : Kallianpur, Gopinath (1925-2015)
Sundar, Padmanabhan
Titre(s) : Stochastic analysis and diffusion processes [Texte imprimé] / Gopinath Kallianpur and P. Sundar
Publication : Oxford : Oxford university press, 2014
Description matérielle : 1 vol. (XI-352 p.) ; 24 cm
Collection : Oxford graduate texts in mathematics ; 24
Lien à la collection : Oxford graduate texts in mathematics
Comprend : Introduction to stochastic processes ; Brownian motion and Wiener measure ; Elements
of martingale theory ; Analytic tools for Brownian motion ; Stochastic integration
; Stochastic differential equations ; The martingale problem ; Probability theory
and partial differential equations ; Gaussian solutions ; Jump Markov processes
; Invariant measures and ergodicity ; Large deviations for diffusions.
Note(s) : Bibliogr. p. 347-350
"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."
Sujet(s) : Analyse stochastique
Processus de diffusion
Indice(s) Dewey :
519.233 (23e éd.) = Processus de Markov
Identifiants, prix et caractéristiques : ISBN 9780199657063. - ISBN 0199657068 (rel.). - ISBN 9780199657070. - ISBN 0199657076
(br.)
Identifiant de la notice : ark:/12148/cb437648475
Notice n° :
FRBNF43764847
(notice reprise d'un réservoir extérieur)
