SPDEs driven by Poisson random measure with non Lipschitz coefficients: existence results

• 成果类型: Article
• 署名作者: Hausenblas, Erika
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-006-0501-8
• 发表日期: 2007
• 页码: 161-200
• 关键词: differential-equation driven; heat-equation

摘要

The article deals with SPDEs driven by Poisson random measure with non Lipschitz coefficients. Let A : E -> E be a generator of an analytic semigroup on E, E being a certain Banach space. Let (Omega, F, (F-t)(t >= 0), P) be a stochastic basis carrying an E-valued Poisson random measure eta with characteristic measure v and compensator gamma. Let 1 <= p <= 2. Our point of interest is the existence of solutions to SPDE's of e.g. the following type [GRAPHICS] where g : E -> L (E, E-0) is some mapping satisfying integral(E)vertical bar g(x, z) - g(y, z)vertical bar(p)upsilon(dz) < C vertical bar x - y vertical bar(rp), x, y is an element of E, where 0 < r < 1 satisfy certain condition specified later and E-0 subset of E is again a certain Banach space.