Sankhya: The Indian Journal of Statistics
1999, Volume 61, Series A, Pt. 1 ,pp. 12--35
STABILITY AND FUNCTIONAL LIMIT THEOREMS FOR RANDOM DEGENERATE DIFFUSIONS
GOPAL K. BASAK , ARNAB BISI
Hong Kong University of Science and Technology, Kowloon
MRINAL K. GHOSH Indian Institute of Science, Bangalore
SUMMARY.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 Markov chain. Under a Liapunov type condition we establish certain growth properties and asymptotic flatness of the flow. This yields the existence of a unique invariant probability p and stability in distribution. We then identify a broad subset of L2($\RR$d * Q,p) which belongs to the range of the infinitesimal generator of the random diffusion. For functions in this set we derive the functional central limit theorem and the law of iterated logarithm
AMS (1991) subject classification. 60F17, 60J60.
Key words and phrases. Random diffusions, Markov chain, tightness, stability, functional central limit theorem, law of iterated logarithm.
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