ON STRONG SOLUTIONS OF ITO'S EQUATIONS WITH sigma is an element of W-d(1) AND b is an element of L-d

We consider Ito uniformly nondegenerate equations with time independent coefficients, the diffusion coefficient in W-d,loc(1) and the drift in L-d. We prove the unique strong solvability for any starting point and prove that, as a function of the starting point, the solutions are Holder continuous w...

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Veröffentlicht in:	The Annals of probability 2021-11, Vol.49 (6), p.3142-3167
1. Verfasser:	Krylov, N.
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Sprache:	eng
Schlagworte:	Mathematics Physical Sciences Science & Technology Statistics & Probability
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description	We consider Ito uniformly nondegenerate equations with time independent coefficients, the diffusion coefficient in W-d,loc(1) and the drift in L-d. We prove the unique strong solvability for any starting point and prove that, as a function of the starting point, the solutions are Holder continuous with any exponent < 1. We also prove that if we are given a sequence of coefficients converging in an appropriate sense to the original ones, then the solutions of approximating equations converge to the solution of the original one.
doi_str_mv	10.1214/21-AOP1525
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subjects	Mathematics Physical Sciences Science & Technology Statistics & Probability
title	ON STRONG SOLUTIONS OF ITO'S EQUATIONS WITH sigma is an element of W-d(1) AND b is an element of L-d
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