Tions like these involving stochastic differentials example 1 according to itos formula the solution of the stochastic differ ential equation dy ydw y0 1 is yt ewt t2 and not. This book provides a quick but very readable introduction to stochastic differential equations that is to differential equations subject to additive white noise and related random disturbances the exposition is strongly focused upon the interplay between probabilistic intuition and mathematical rigour topics include a quick survey of measure theoretic probability theory followed by an introduction to brownian motion and the ito stochastic calculus and finally the theory of stochastic . This chapter also offers an introduction to the mathematical theory of stochastic processes including the notion of continuity measurability stopping times martingaleswiener processes and gaussian processes these concepts enable us to define the so called ito integral the ito formula and diffusion processes. An introduction to stochastic differential equations version 12 lawrencecevans departmentofmathematics ucberkeley chapter1 introduction chapter2