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

A class of stochastic differential equations given by dx(t) = f(x(t))dt + g(x(t))dW(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.