Existence and uniquenesstheorems for some stochastic parabolic partial differential equations

Abstract

In this paper we will prove existence and uniqueness heorems for the stochastic differential equations

with initial conditions is a white noise vector is positive white noise is a positive white noise matrix and f, g are real functions. We will show that these equations have solutions in the space (S)^-1of generalized white noise distributions in a strong differentiation sense

Keywords:

• Generalized white noise distributions
• Wick product
• Hermite Transform