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Licensed Unlicensed Requires Authentication Published by De Gruyter February 23, 2010

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

  • H. J. Engelbert and V. P. Kurenok

Abstract

We study multidimensional stochastic equations

where xo 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.

Received: 2000-07-24
Published Online: 2010-02-23
Published in Print: 2000-December

© Heldermann Verlag

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