Stochastic Processes and SomeApplications

Abstract

In this research we study Brownian motion and we discuss continuity and Holder continuity of Brownian paths, and local martingales. We present some simple integrands and processes and L^2 properties, and we applied Brownian motion on Ito’s integrals and formulas, and we also discuss some applications to Brownian motion and martingales. Then we discuss relation between Brownian motion and differential equations.