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Original Articles

Penalization methods for reflecting stochastic differential equations with jumps

Pages 275-293 | Received 31 May 2002, Accepted 29 Apr 2003, Published online: 21 Aug 2006
 

Abstract

The problem of approximation of a solution to a reflecting stochastic differential equation (SDE) with jumps by a sequence of solutions to SDEs with penalization terms is considered. The approximating sequence is not relatively compact in the Skorokhod topology J 1 and so the methods of approximation based on the J 1-topology break down. In the paper, we prove our convergence results in the S-topology on the Skorokhod space D(R+, R d ) introduced recently by Jakubowski. The S-topology is weaker than J 1 but stronger than the Meyer-Zheng topology and shares many useful properties with J 1.

Acknowledgements

Research partially supported by Komitet Badań Naukowych under grant 0253/P03/2000/19.

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