BSDE on an infinite horizon and elliptic PDEs in infinite dimension

被引：16
|
作者：
Hu, Ying [1 ]
Tessitore, Gianmario [2 ]
机构：
[1] Univ Rennes 1, IRMAR, F-35042 Rennes, France
[2] Univ Milan, Dipartimento Matemat & Applicaz, I-20125 Milan, Italy
来源：
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2007年 / 14卷 / 5-6期
关键词：
backward stochastic differential equations elliptic PDEs; Hilbert spaces; mild solutions;
D O I：
10.1007/s00030-007-6029-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study the existence and uniqueness of mild solutions to a possibly degenerate elliptic partial differential equation Lu(x) + psi(x, u(x), del u(x)G(x)) - lambda u(x) = 0 in Hilbert spaces. Our aim is, in the case in which (-, 0, 0) is bounded, to drop the assumptions on the size of A needed in [11]. The main tool will be existence, uniqueness and regular dependence on parameters of a bounded solution to a suitable backward stochastic differential equation with infinite horizon. Finally we apply the result to study an optimal control problem.
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页码：825 / 846
页数：22
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