Jump-diffusion processes in random environments

Jacek Jakubowski; Mariusz Niewęgłowski

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arXiv · 1305.4129

Jump-diffusion processes in random environments

Jacek Jakubowski·Mariusz Niewęgłowski

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Abstract

In this paper we investigate jump-diffusion processes in random environments which are given as the weak solutions to SDE's. We formulate conditions ensuring existence and uniqueness in law of solutions. We investigate Markov property. To prove uniqueness we solve a general martingale problem for \cadlag processes. This result is of independent interest. In the last section we present application of our results considering generalized exponential Levy model.

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BibTeX RIS

Jacek Jakubowski, Mariusz Niewęgłowski. 2013-07-18. Jump-diffusion processes in random environments. https://arxiv.org/abs/1305.4129

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