Stability and functional limit theorems for random degenerate diffusions

Abstract

We study the stability and functional limit theorems for a class of random degenerate diffusions where the flow is driven by a Wiener process and an independent Markovchain. Under a Liapunov type condition we establish certain growth properties and asymptoticflatness of the flow. This yields the existence of a unique invariant probability p and stabilityin distribution. We then identify a broad subset of L²(IR ^d × Θ, π ) which belongs to the rangeof the infinitesimal generator of the random diffusion. For functions in this set we derive thefunctional central limit theorem and the law of iterated logarithm.