Diffusion equation for multivalued stochastic differential equations

AbstractDeterministic oscillations with bilinear hysteresis are governed by a multivalued differential equation of the type ξ′ + kξ ϵ b(ξ) + g, where k is maximal monotonic and b is Lipschitzian. An existence and uniqueness result is proven for corresponding stochastic equation. The diffusion equation satisfied by the laws of ξ(t) is established. In the particular case k = 0, this equation is equivalent to the Fokker-Planck equation