On strong solutions of Itô's equations with a$\,\in W^{1}_{d}$ and b$\,\in L_{d}$

N. V. Krylov

paper

On strong solutions of Itô's equations with a $\in W_{d}^{1}$ and b $\in L_{d}$

arXiv:2007.06040

Abstract

We consider Itô uniformly nondegenerate equations with time independent coefficients, the diffusion coefficient in $W_{d, l oc}^{1}$ , 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 Hölder 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.

29 pages

References in corpus (1)

Correction to the paper "Some remarks on Davie's uniqueness theorem"

On strong solutions of Itô's equations with a∈Wd1​ and b∈Ld​

Abstract

References in corpus (1)

Cited by in corpus (2)

On strong solutions of Itô's equations with a $\in W_{d}^{1}$ and b $\in L_{d}$