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Jump-diffusion processes in random environments |
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| Authors: | Jacek Jakubowski Mariusz Niewęgłowski |
| Affiliation: | 1. Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02-097 Warszawa, Poland;2. Faculty of Mathematics and Information Science, Warsaw University of Technology, ul. Koszykowa 75, 00-662 Warszawa, Poland;3. Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA |
| Abstract: | In this paper we investigate jump-diffusion processes in random environments which are given as the weak solutions of SDEs. We formulate conditions ensuring existence and uniqueness in law of solutions. We investigate the Markov property. To prove uniqueness we solve a general martingale problem for càdlàg processes. This result is of independent interest. Application of our results to generalized exponential Lévy model are present in the last section. |
| Keywords: | 60H20 60H30 60J65 60G55 60G50 |
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