Rough paths and 1d SDE with a time dependent distributional drift: application to polymers

• 成果类型: Article
• 署名作者: Delarue, Francois; Diel, Roland
• 署名单位: Universite Cote d'Azur; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-015-0626-8
• 发表日期: 2016
• 页码: 1-63
• 关键词: simple random-walk; Local Time; EQUATIONS; diffusion

摘要

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 -Holder 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.