Sankhya: The Indian Journal of Statistics

2001, Volume 63, Series A, Pt. 2, pp. 194--228

STRATONOVICH TYPE SDE'S WITH NORMAL REFLECTION DRIVEN BY SEMIMARTINGALES

By

ARTURO KOHATSU-HIGA, Universitat Pompeu Fabra, Barcelona, Spain

SUMMARY. We define a generalized normally reflecting diffusion process of Stratonovich type driven by a general semimartingale with jumps on a bounded domain. The model is defined so that it does not require any condition on the jump size of the driving semimartingale when the domain is smooth. For non-smooth domains we require the semimartingale to have summable jumps. Besides studying the existence of uniqueness for the stochastic differential equations that defines such processes we also give results on the Markov property of the solutions as well as some stability properties of this model.

AMS (1991) subject classification. Primary 60H10, 60J75; secondary 60J25, 60J60.

Key words and phrases. Reflected s.d.e.'s, semimartingales, jump processes, Markov property, stability properties.

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