On Multidimensional SDEs Without Drift and with A Time-Dependent Diffusion Matrix

Autor:	V. P. Kurenok, H. J. Engelbert
Rok vydání:	2000
Předmět:	Matrix (mathematics) Time dependent diffusion General Mathematics Mathematical analysis Mathematics
Zdroj:	Georgian Mathematical Journal. 7:643-664
ISSN:	1572-9176 1072-947X
DOI:	10.1515/gmj.2000.643
Popis:	We study multidimensional stochastic equations where x o is an arbitrary initial state, W is a d-dimensional Wiener process and is a measurable diffusion coefficient. We give sufficient conditions for the existence of weak solutions. Our main result generalizes some results obtained by A. Rozkosz and L. Słomiński [Stochastics Stochasties Rep. 42: 199–208, 1993] and T. Senf [Stochastics Stochastics Rep. 43: 199–220, 1993] for the existence of weak solutions of one-dimensional stochastic equations and also some results by A. Rozkosz and L. Słomiński [Stochastic Process. Appl. 37: 187–197, 1991], [Stochastic Process. Appl. 68: 285–302, 1997] for multidimensional equations. Finally, we also discuss the homogeneous case.
Databáze:	OpenAIRE
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