Homogeneous Stochastic Differential Equations

Abstract

We study the relation between solutions to a certain type of nonlinear partial differential equation and solutions to its stochastic analogy driven by a fractional Brownian motion with Hurst index H > 1/2. The formula obtained is used to study properties of solutions to some stochastic differential equations, such as the stochastic porous medium equation.

Keywords

• stochastic differential equation
• fractional Brownian motion
• homogeneous function