Multidimensional SDEs with singular drift and universal construction of the polymer measure with white noise potential
type: Item
instance of: scholarly article
title: Multidimensional SDEs with singular drift and universal construction of the polymer measure with white noise potential
zbMATH Open document ID: 1407.60109
DOI: 10.1214/17-AOP1213
author: G. Cannizzaro
author: Khalil Chouk
published in: The Annals of Probability
publication date: 2018-06-26T00:00:00Z
full work available at URL: https://arxiv.org/abs/1501.04751
full work available at URL: https://projecteuclid.org/euclid.aop/1523520027
review text: The authors consider a stochastic differential equation of the form \(dX_t=V(t, X_t)+dB_t, \,\, X_0=x\), where \(B\) is a \(d\)-dimensional Brownian motion, \(x\) is a point in \(\mathbb R^d\) and \(V\) is a function of time taking values in the space of distributions. They study the existence and uniqueness of the solution by giving a meaning to the Strook-Varadhan martingale problem associated with the equation. The paracontrolled distributions approach introduced in [\textit{M. Gubinelli} et al., Forum Math. Pi 3, Article ID e6, 75 p. (2015; Zbl 1333.60149)] is applied. The examples include the case when a 2 and 3-dimensional polymer measure with white noise potential can be constructed.
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 60H15
zbMATH DE Number: 6894784
zbMATH Keywords: singular SDEs
zbMATH Keywords: singular SPDEs
zbMATH Keywords: paracontrolled calculus
zbMATH Keywords: polymer measure
reviewed by: Alexandra Rodkina
MaRDI profile type: Publication
arXiv ID: 1501.04751
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Wikidata QID: Q129985841
description: scientific article