Adapted solution of a backward semilinear stochastic evolution equation
- 1 January 1991
- journal article
- research article
- Published by Taylor & Francis in Stochastic Analysis and Applications
- Vol. 9 (4) , 445-459
- https://doi.org/10.1080/07362999108809250
Abstract
Let K and H be two separable Hilbert spaces and be a cylindrical Wiener process with values in K defined on a probability space denote its natural filtration. Given , we look for an adapted pair of process with values in H and respectively is defined in §1),which solves a semilinear stochastic evolution equation of the backward form: where A is the infinitesimal generators of a C 0-semigroup {eAt } on H. The precise meaning of the equation is A linearized version of that equation appears in infinite-dimensional stochastic optimal control theory as the equation satisfied by the adjoint process. We also give our results to the following backward stochastic partial differential equation:Keywords
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