WHITE NOISE CALCULUS IN APPLICATIONS TO STOCHASTIC EQUATIONS IN HILBERT SPACES

摘要

Stochastic differential equations arise in numerous applications as mathematical models reflecting the random influence of white noise type on a system under consideration. We will further restrict ourselves to the case of Gaussian white noise. The intention to introduce noise into a differential equation meets several obstacles one of which is connected with the fact that the white noise process is (informally) defined as a random process whose values at different t are independent identically distributed random variables with mean values equal to zero and infinite deviations. This means that the white noise is not a random process in the usual sense.