MPS-RR 2002-47
December 2002

Solving Stochastic Jump Differential Equations

by:

Pavel V. Gapeev

Abstract

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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