Some methods of integration in function space for use in control and filtering

Recently stochastic methods have been found that establish existence and smoothness of the density for the probability distribution of a solution of a stochastic differential equation. Since such a question often arises in stochastic control and stochastic filtering, these stochastic methods will be described in this paper. Different and more elementary proofs will be given for some of the basic tools of these stochastic methods. The approach in this paper will be related to the interplay between quantum mechanics and quantum field theory.