Annals of Probability
- Ann. Probab.
- Volume 32, Number 1B (2004), 607-660.
Infinite horizon backward stochastic differential equations and elliptic equations in Hilbert spaces
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.
Ann. Probab., Volume 32, Number 1B (2004), 607-660.
First available in Project Euclid: 11 March 2004
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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