Introduction to Stochastic Analysis

This is an introduction to stochastic integration and stochasticdifferential equations written in an understandable way for a wideaudience, from students of mathematics to practitioners in biology, chemistry, physics, and finances. The presentation is based on thenaïve stochastic integration, rather than on abstract theoriesof measure and stochastic processes. The proofs are rather simplefor practitioners and, at the same time, rather rigorous formathematicians. Detailed application examples in natural sciencesand finance are presented. Much attention is paid to simulationdiffusion processes. The topics covered include Brownian motion; motivation ofstochastic models with Brownian motion; Itô and Stratonovichstochastic integrals, Itô's formula; stochasticdifferential equations (SDEs); solutions of SDEs as Markovprocesses; 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.