Irina V. Melnikova, Valentina S. Parfenenkova
Abstract:
In this article we study the relationship between solutions to Cauchy problems
for the abstract stochastic differential equation
and solutions to Cauchy problems (backward and forward)
for the infinite dimensional deterministic partial differential equation
where g is the probability characteristic
in the backward case and
in the forward case.
This relationship, that is the inifinite dimensional Feynman-Kac theorem,
is proved in both directions: from stochastic to deterministic and from
deterministic to stochastic. Special attention is given to the definition and
interpretation of objects in the equations.
Submitted February 20, 2014. Published October 7, 2014.
Math Subject Classifications: 47D06, 60G15, 60H30.
Key Words: Semigroups of operators; infinite dimensional stochastic equations;
diffusion processes; Kolmogorov equations.
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Irina V. Melnikova Ural Federal University Lenin av. 51, 620083 Ekaterinburg, Russia email: Irina.Melnikova@usu.ru | |
Valentina S. Parfenenkova Ural Federal University Lenin av. 51, 620083 Ekaterinburg, Russia email: vika8887@e1.ru |
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