Stability and functional limit theorems for random degenerate diffusions

Basak, Gopal K. ; Bisi, Arnab ; Ghosh, Mrinal K. (1999) Stability and functional limit theorems for random degenerate diffusions Sankhya - Series A, 61 (1). pp. 12-35. ISSN 0581-572X

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Official URL: http://www.jstor.org/stable/10.2307/25051226

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.

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