Affiliation:
1. Institute of Mathematics, EPFL, Bâtiment MA, Lausanne, 1015 VD, Switzerland
Abstract
Recently Krylov [N. V. Krylov, On time inhomogeneous stochastic Itô equations with drift in [Formula: see text], Ukraïn. Mat. Zh. 72 (2020) 1232–1253] established weak existence of solutions to SDEs for integrable drifts in mixed Lebesgue spaces, whose exponents satisfy the condition [Formula: see text], thus going below the celebrated Ladyzhenskaya–Prodi–Serrin condition. We present here a variant of such result, whose proof relies on an alternative technique, based on a partial Zvonkin transform; this allows for drifts with growth at infinity and/or in uniformly local Lebesgue spaces.
Publisher
World Scientific Pub Co Pte Ltd