Penalization methods for reflecting stochastic differential equations with jumps

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.

Keywords:

• Reflecting stochastic differential equation
• Penalization method
• Skorokhod problem
• Stochastic differential equation
• primary 60H20
• secondary 60F17

Acknowledgements

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