Existence and uniqueness of solution for a class of stochastic differential equations

Abstract

A class of stochastic differential equations given by d x (t) = f (x (t)) d t + g (x (t)) d W (t), x (t 0) = x 0, t 0 ≤ t ≤ T < + ∞, are investigated. Upon making some suitable assumptions, the existence and uniqueness of solution for the equations are obtained. Moreover, the existence and uniqueness of solution for stochastic Lorenz system, which is illustrated by example, are in good agreement with the theoretical analysis. © 2013 Junfei Cao et al.