1. Time-symmetric optimal stochastic control problems in space-time domains.
- Author
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Cruzeiro, Ana Bela, Oliveira, Carlos, and Zambrini, Jean-Claude
- Subjects
- *
STOCHASTIC control theory , *SPACETIME , *STOCHASTIC processes - Abstract
We present a pair of adjoint optimal control problems characterizing a class of time-symmetric stochastic processes defined on random time intervals. The associated PDEs are of free-boundary type. The particularity of our approach is that it involves two adjoint optimal stopping times adapted to a pair of filtrations, the traditional increasing one and another, decreasing. They are the keys of the time symmetry of the construction, which can be regarded as a generalization of 'Schrödinger's problem' (1931–1932) to space-time domains. The relation with the notion of 'Hidden diffusions' is also described. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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