Some parabolic pdes whose drift is an irregular random noise in space

• 成果类型: Article
• 署名作者: Russo, Francesco; Trutnau, Gerald
• 署名单位: Universite Paris 13; University of Bielefeld
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117906000001178
• 发表日期: 2007
• 页码: 2213-2262
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; integration; calculus

摘要

A new class of random partial differential equations of parabolic type is considered, where the stochastic term consists of an irregular noisy drift, not necessarily Gaussian, for which a suitable interpretation is provided. After freezing a realization of the drift (stochastic process), we study existence and uniqueness (in some appropriate sense) of the associated parabolic equation and a probabilistic interpretation is investigated.