On Multidimensional SDEs Without Drift and with A Time-Dependent Diffusion Matrix
2000 ◽
Vol 7
(4)
◽
pp. 643-664
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Keyword(s):
Abstract 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.
2006 ◽
Vol 220
(2)
◽
pp. 322-353
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2021 ◽
Vol 39
(2)
◽
pp. 400-406
1982 ◽
Vol 26
(4)
◽
pp. 670-686
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2016 ◽
Vol 1
(1)
◽
pp. 8-17