Non-linear rough heat equations

• 成果类型: Article
• 署名作者: Deya, A.; Gubinelli, M.; Tindel, S.
• 署名单位: Universite PSL; Universite Paris-Dauphine; Universite de Lorraine
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-011-0341-z
• 发表日期: 2012
• 页码: 97-147
• 关键词: fractional brownian-motion; evolution-equations; stochastic calculus; driven; integration; spdes; wave

摘要

This article is devoted to define and solve an evolution equation of the form dy (t) = Delta y (t) dt + dX (t) (y (t) ), where Delta stands for the Laplace operator on a space of the form , and X is a finite dimensional noisy nonlinearity whose typical form is given by , where each x = (x ((1)), aEuro broken vertical bar , x ((N))) is a gamma-Holder function generating a rough path and each f (i) is a smooth enough function defined on . The generalization of the usual rough path theory allowing to cope with such kind of system is carefully constructed.