Existence and uniqueness theorems for some stochastic parabolic partial differential equations

In this paper we will prove existence and uniqueness theorems for the stochastic differential equations [GRAPHICS] with initial conditions u(O,x) = f(x) For All x is an element of R-n where (W) over right arrow W-phi(t,W- x) is a white noise vector, Exp{W-phi(t,W- x)} is positive white noise, Exp{W-phi?S(t,W-x)} is a positive white noise matrix and f, g are real functions. We will show that these equations have solutions in the space (S)(-1) of generalized white noise distributions in a strong differentiation sense.