ON MULTIDIMENSIONAL SDEs WITHOUT DRIFT AND WITH TIME-DEPENDENT DIFFUSION MATRIX
نویسنده
چکیده
We study multidimensional stochastic equations Xt = x0 + ∫ t 0 B(s,Xs) dWs where x0 is an arbitrary initial state, W is a d-dimensional Wiener process and B : [0, +∞) × IR → IRd2 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. S lomiński [17] and T. Senf [20] for the existence of weak solutions of one-dimensional stochastic equations and also some results by A. Rozkosz and L. S lomiński [18], [19] for multidimensional equations. Finally, we also discuss the homogeneous case.
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تاریخ انتشار 2003