Penalization methods for the Skorokhod problem and reflecting SDEs with jumps

Weronika Łaukajtys; Leszek Słomiński

doi:10.3150/12-BEJ428

Penalization methods for the Skorokhod problem and reflecting SDEs with jumps

Statistics Theory 2013-12-11 v1 Statistics Theory

Authors: Weronika Łaukajtys , Leszek Słomiński

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Abstract

We study the problem of approximation of solutions of the Skorokhod problem and reflecting stochastic differential equations (SDEs) with jumps by sequences of solutions of equations with penalization terms. Applications to discrete approximation of weak and strong solutions of reflecting SDEs are given. Our proofs are based on new estimates for solutions of equations with penalization terms and the theory of convergence in the Jakubowski $S$ -topology.

Keywords

Skorokhod problem reflecting SDEs jumps penalization methods discrete approximation Jakubowski S-topology stochastic differential equations

Cite

@article{arxiv.1312.2794,
  title  = {Penalization methods for the Skorokhod problem and reflecting SDEs with jumps},
  author = {Weronika Łaukajtys and Leszek Słomiński},
  journal= {arXiv preprint arXiv:1312.2794},
  year   = {2013}
}

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Published in at http://dx.doi.org/10.3150/12-BEJ428 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

Penalization methods for the Skorokhod problem and reflecting SDEs with jumps

Abstract

Keywords

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