Solutions to stochastic differential equations depends on the method of approximation. In this paper we give a very simple demonstration that ordinary differential equations, too, exhibit this kind of behavior when the coefficients are measure-valued distributions. We then proceed to show that...

In this paper we consider continuity properties of a stochastic heat equation of the form [not partial differential]u(t,x)/[not partial differential]t = [not partial differential]2u(t,x)/[not partial differential]x2 + f(u(t,x))Wx,t. We prove that the solutions of this equation depend...