Reflecting stochastic differential equations with jumps

Arturo Kohatsu-Higa, Purdue University

Abstract

Lions and Sznitman (1984) studied diffusions reflected at the boundary of a domain in $R\sp{d}.$ Saisho extended their results by weakening the conditions on the boundary of the domain. Later, Menaldi and Robin (1985) published results on stochastic differential equations driven by a Levy process with reflection at the boundary of a domain. The main condition Menaldi and Robin imposed on the Levy process is that the jumps of the process have to put the solution process inside the domain. We study a different model for stochastic differential equations driven by general semimartingales with reflection. This model introduced by Kurtz, Pardoux and Protter (1992), called Stratonovich type stochastic differential equation, imposes weaker conditions than those in Menaldi and Robin (1985) when reflection is considered. We also study stability results and the time reversal of the solutions of Stratonovich type stochastic differential equations with reflection.

Degree

Ph.D.

Advisors

Protter, Purdue University.

Subject Area

Statistics

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