Boundary value problems for functionals of Ito processes
Nikolai Dokuchaev
TL;DR
This paper investigates backward stochastic partial differential equations related to Ito processes, establishing existence, regularity, duality with forward SPDEs, and representing functionals of Ito processes in various domains.
Contribution
It provides new existence and regularity results for backward SPDEs and explores their duality with forward SPDEs, along with representation techniques for Ito process functionals.
Findings
Existence and regularity of solutions to backward SPDEs established.
Duality relationship between backward and forward SPDEs demonstrated.
Representation formulas for functionals of Ito processes discussed.
Abstract
Backward stochastic partial differential equations in bounded and unbounded domains are studied. Existence and regularity results are obtained. Duality relationship with forward SPDEs are established. Representation of functionals of Ito processes in bounded domains is discussed.
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