Strong solutions of stochastic equations with singular time dependent drift
type: Item
instance of: scholarly article
title: Strong solutions of stochastic equations with singular time dependent drift
zbMATH Open document ID: 1072.60050
publication date: 2005-03-17T00:00:00Z
review text: Existence and uniqueness of solutions to stochastic differential equations in domains \(G \subset {\mathbb R}^d\) with unit local diffusion and singular time dependent drift \(b\) up to an explosion time are proved under the assumption of local \(L_{q^-}L_p \equiv L_q({\mathbb R}, L_p)\)-integrability on \(b\) in \({\mathbb R} \times G\) with \(d/p + 2/q < 1\). Strong Feller properties are also proved for this case. In the case when \(b\) is the gradient in \(x\) of a nonnegative function \(\psi\) blowing up as \(G \ni x\to \partial G\), it is proved that the conditions \(2D_t \psi \leq K \psi\), \(2 D_t \psi + \Delta \psi \leq K e^{\varepsilon \psi}\), \(\varepsilon \in [0, 2)\), imply that the explosion time is infinite and the distributions of the solution have sub-Gaussian tails.
Mathematics Subject Classification ID: 60H20
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 35R60
zbMATH DE Number: 2146837
zbMATH Keywords: stochastic differential equations
zbMATH Keywords: singular drift
zbMATH Keywords: distorted Brownian motion
author: N. V. Krylov
author: Michael Röckner
reviewed by: Pavel Gapeev
MaRDI profile type: Publication
full work available at URL: s00440-004-0361-z
OpenAlex ID: W2026968525
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DOI: 10.1007/S00440-004-0361-Z
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 2146837