Infinite horizon backward stochastic differential equations and elliptic equations in Hilbert spaces
成果类型：
Article
署名作者：
Fuhrman, M; Tessitore, G
署名单位：
Polytechnic University of Milan; University of Parma
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
发表日期：
2004
页码：
607-660
关键词：
摘要：
Solutions of semilinear elliptic differential equations in infinite-dimensional spaces are obtained by means of forward and backward infinite-dimensional stochastic evolution equations. The backward equation is considered on an infinite time horizon and a suitable growth condition replaces the final condition. Elliptic equations are intended in a mild sense, suitable also for applications to optimal control. We finally notice that, due to the lack of smoothing properties, the elliptic partial differential equation considered here could not be treated by analytic methods.