Annals of Probability

Infinite horizon backward stochastic differential equations and elliptic equations in Hilbert spaces

Marco Fuhrman and Gianmario Tessitore

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Abstract

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.

Article information

Source
Ann. Probab., Volume 32, Number 1B (2004), 607-660.

Dates
First available in Project Euclid: 11 March 2004

Permanent link to this document
https://projecteuclid.org/euclid.aop/1079021459

Digital Object Identifier
doi:10.1214/aop/1079021459

Mathematical Reviews number (MathSciNet)
MR2039938

Zentralblatt MATH identifier
1046.60061

Subjects
Primary: 60H30: Applications of stochastic analysis (to PDE, etc.) 35R15: Partial differential equations on infinite-dimensional (e.g. function) spaces (= PDE in infinitely many variables) [See also 46Gxx, 58D25]
Secondary: 93E20: Optimal stochastic control 49L99: None of the above, but in this section

Keywords
Backward stochastic differential equations partial differential equations in infinite-dimensional spaces Hamilton--Jacobi--Bellman equation stochastic optimal control in infinite horizon

Citation

Fuhrman, Marco; Tessitore, Gianmario. Infinite horizon backward stochastic differential equations and elliptic equations in Hilbert spaces. Ann. Probab. 32 (2004), no. 1B, 607--660. doi:10.1214/aop/1079021459. https://projecteuclid.org/euclid.aop/1079021459


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