Stochastic Undergraduate

Authors: Le Gall, Jean-François
Provides a concise and rigorous presentation of stochastic integration and stochastic calculus for continuous semimartingales
Presents major applications of stochastic calculus to Brownian motion and related stochastic processes
Includes important aspects of Markov processes with applications to stochastic differential equations and to connections with partial differential equations

An interdisciplinary approach to understanding queueing and graphical networks
In today's era of interdisciplinary studies and research activities, network models are becoming increasingly important in various areas where they have not regularly been used.

The subjects of stochastic processes, information theory, and Lie groups are usually treated separately from each other. This unique two-volume set presents these topics in a unified setting, thereby building bridges between fields that are rarely studied by the same people. Unlike the many excellent formal treatments available for each of these subjects individually, the emphasis in both of these volumes is on the use of stochastic, geometric, and group-theoretic concepts in the modeling of physical phenomena.

This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter.