Rough paths and 1d SDE with a time dependent distributional drift: application to polymers
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Publication:292116
DOI10.1007/S00440-015-0626-8zbMATH Open1462.60121arXiv1402.3662OpenAlexW2006672523MaRDI QIDQ292116
Author name not available (Why is that?)
Publication date: 10 June 2016
Published in: (Search for Journal in Brave)
Abstract: Motivated by the recent advances in the theory of stochastic partial differential equations involving nonlinear functions of distributions, like the Kardar-Parisi-Zhang (KPZ) equation, we reconsider the unique solvability of one-dimensional stochastic differential equations, the drift of which is a distribution, by means of rough paths theory. Existence and uniqueness are established in the weak sense when the drift reads as the derivative of a H{"o}lder continuous function. Regularity of the drift part is investigated carefully and a related stochastic calculus is also proposed, which makes the structure of the solutions more explicit than within the earlier framework of Dirichlet processes.
Full work available at URL: https://arxiv.org/abs/1402.3662
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