Sankhya: The Indian Journal of Statistics

2001, Volume 63, Series A, Pt. 2, pp. 139--177

THE INTERLACING CONSTRUCTION FOR STOCHASTIC FLOWS OF DIFFEOMORPHISMS ON EUCLIDEAN SPACES

By

DAVID APPLEBAUM and FUCHANG TANG Nottingham Trent University, Nottingham, England

SUMMARY. We investigate stochastic differential equations driven by infinite-dimensional semimartingales with jumps and show that both the solution flow and the derivative flow can be represented as almost-sure limits of sequences that consist of random motion with continuous sample paths which are interlaced with random jumps. We are thus able to obtain new transparent proofs of the diffeomorphism property of such flows.

AMS (1991) subject classification. 60H10, 60H05, 60G55, 60G44.

Key words and phrases. Semimartingale, stochastic flow, diffeomorphism, exponential map, interlacing construction.

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