Translation Invariant Diffusions and Stochastic Partial Differential Equations in ${\cal S}^{\prime}

Abstract

In this article we show that the ordinary stochastic differential equations of K.Itô maybe considered as part of a larger class of second order stochastic PDE's that are quasi linear and have the property of translation invariance. We show using the `monotonicity inequality' and the Lipshitz continuity of the coefficients ${\sigma }_{ij}$ and $b_i$, existence and uniqueness of strong solutions for these stochastic PDE's. Using pathwise uniqueness, we prove the strong Markov property.

In the new version, some typos have been corrected, minor notational changes have been made and the reference list updated

References in corpus (1)

• Invariance of closed convex cones for stochastic partial differential equations