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Centre for Mathematical Physics and Stochastics
Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

MPS-RR 2002-47
December 2002

Solving Stochastic Jump Differential Equations


Pavel V. Gapeev


We present a reducibility criterion for stochastic differential equations driven by both a Wiener process and a Poisson random measure to equations with linear diffusion coefficients having explicit solutions or reducible to ordinary equations. We construct jump analogues of continuous diffusions satisfying equations of the type mentioned above and show that the obtained processes have the same supports of marginal distributions as the initial processes. We also illustrate the action of this method on some diffusions.

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