Evolution equation of a stochastic semigroup with white-noise drift

• 成果类型: Article
• 署名作者: Nualart, D; Viens, F
• 署名单位: University of Barcelona; University of North Texas System; University of North Texas Denton
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2000
• 页码: 36-73
• 关键词: partial-differential equations; calculus

摘要

We study the existence and uniqueness of the solution of a function-valued stochastic evolution equation based on a stochastic semigroup, whose kernel p(s, t, y, x) is Brownian in s and t. The kernel p is supposed to be measurable with respect to the increments of an underlying Wiener process in the interval [s, t]. The evolution equation is then anticipative and, choosing the Skorohod formulation, we establish existence and uniqueness of a continuous solution with values in L-2(R-d). As an application we prove the existence of a mild solution of the stochastic parabolic equation du(t) = Delta(x)udt + v(dt, x) . del u + F(t, x, u)W(dt, x), where v and W are Brownian in time with respect to a common filtration. In this case, p is the formal backward heat kernel of Delta(x) + v(dt, x) . del(x).