Stochastic differential equations
of the type (written symbolically)
(1.1)
where z(t) is Brownian motion, arise in physics and engineering and are also the
object of study of pure mathematicians. In this paper it will be shown that the
integral associated with the distribution of the function x(⋅) may be expressed in
terms of a Wiener integral with a weighting functional (the Radon-Nikodym
derivative). Thus the expected values of functionals with respect to the distribution
of x(⋅) can be easily and concisely expressed. Also it will be shown that certain
partial differential equations of physics naturally have their solutions associated with
this integral.
