Rough path stability of (semi-)linear SPDEs

• 成果类型: Article
• 署名作者: Friz, Peter; Oberhauser, Harald
• 署名单位: Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Technical University of Berlin
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-013-0483-2
• 发表日期: 2014
• 页码: 401-434
• 关键词: partial-differential-equations; wong-zakai approximations; evolution-equations; stochastic-analysis; support theorem; driven; signals; AREA

摘要

We give meaning to linear and semi-linear (possibly degenerate) parabolic partial differential equations with (affine) linear rough path noise and establish stability in a rough path metric. In the case of enhanced Brownian motion (Brownian motion with its L,vy area) as rough path noise the solution coincides with the standard variational solution of the SPDE.