Brownian Motion and Stochastic Calculus (Graduate Texts in Mathematics)

Description:

This book is designed for a graduate course in stochastic processes. It is written for the reader who is familiar with measure-theoretic probability and the theory of discrete-time processes who is now ready to explore continuous-time stochastic processes. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a Markov process and a martingale in continuous time. The authors show how, by means of stochastic integration and random time change, all continuous martingales and many continuous Markov processes can be represented in terms of Brownian motion. The text is complemented by a large number of exercises.

subjects: Brownian motion processes,  Stochastic analysis,  Brownsche Bewegung,  Processus stochastique,  Équation différentielle stochastique,  Processus de Mouvement brownien,  Mouvement brownien,  Stochastik,  EDP,  Stochastischer Prozess,  Calcul stochastique,  Analyse stochastique,  Stetigkeit,  Stochastische Analysis,  Processus stochastiques,  Brownian movements,  Mathematics,  Distribution (Probability theory),  Probability Theory and Stochastic Processes,  Análisis estocástico,  Brownse beweging,  Stochastische analyse