Diffusion equations in duals of nuclear spaces

Abstract

A stochastic Galerkin method is used to establish the existence of a solution to a martingale problem posed by an Ito type stochastic differential equation for processes taking values in the dual of a nuclear space. Uniqueness of the strong solution is also shown using the monotonicity condition. An application to the motion of random strings is discussed.

Keywords:

• Nuclear space
• diffusion
• martingale problem
• Galerkin method