On the Uniqueness of Solution to Homogeneous SPDEs

Abstract

We study homogeneous stochastic partial differential equations driven by a fractional Brownian motion with Hurst index H greater than 1/2. We state that there is a one-to-one correspondece between solutions to homogeneous stochastic equation and its deterministic counterpart.

In particular, we show that if the deterministic equation has a unique solution, so does the stochastic one.

Keywords

• stochastic differential equation
• fractional Brownian motion
• homogeneous function