Ebooks for the Classroom+Faculty

Introduction to Stochastic Analysis : Integrals and Differential Equations
ISBN: 9781118603338
Platform/Publisher: WOL / John Wiley & Sons, Ltd
Digital rights: Users: Unlimited; Printing: Unlimited; Download: Unlimited
Subjects: Mathematics & Statistics; Mathematics;

This is an introduction to stochastic integration and stochastic differential equations written in an understandable way for a wide audience, from students of mathematics to practitioners in biology, chemistry, physics, and finances. The presentation is based on the naïve stochastic integration, rather than on abstract theories of measure and stochastic processes. The proofs are rather simple for practitioners and, at the same time, rather rigorous for mathematicians. Detailed application examples in natural sciences and finance are presented. Much attention is paid to simulation diffusion processes.
The topics covered include Brownian motion; motivation of stochastic models with Brownian motion; Itô and Stratonovich stochastic integrals, Itô's formula; stochastic differential equations (SDEs); solutions of SDEs as Markov processes; application examples in physical sciences and finance; simulation of solutions of SDEs (strong and weak approximations). Exercises with hints and/or solutions are also provided.

Vigirdas Mackevièius is a professor of Faculty of Mathematics and Informatics at Vilnius University in Lithuania.