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January 2004 Infinite horizon backward stochastic differential equations and elliptic equations in Hilbert spaces
Marco Fuhrman, Gianmario Tessitore
Ann. Probab. 32(1B): 607-660 (January 2004). DOI: 10.1214/aop/1079021459

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.

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Marco Fuhrman. Gianmario Tessitore. "Infinite horizon backward stochastic differential equations and elliptic equations in Hilbert spaces." Ann. Probab. 32 (1B) 607 - 660, January 2004. https://doi.org/10.1214/aop/1079021459

Information

Published: January 2004
First available in Project Euclid: 11 March 2004

zbMATH: 1046.60061
MathSciNet: MR2039938
Digital Object Identifier: 10.1214/aop/1079021459

Subjects:
Primary: 35R15, 60H30
Secondary: 49L99, 93E20

Rights: Copyright © 2004 Institute of Mathematical Statistics

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Vol.32 • No. 1B • January 2004
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