Clark representation formula for the solution to equation with interaction
Jasmina {\DJ}or{\dj}evi\'c, Andrey Dorogovtsev
TL;DR
This paper extends the Clark-Ocone representation to solutions of measure-valued equations involving interaction, demonstrating the integrand's absolute continuity with respect to Lebesgue measure.
Contribution
It introduces a Clark-Ocone representation for measure-valued equations with interaction, establishing the absolute continuity of the integrand.
Findings
Proves the Clark-Ocone representation for the solution.
Shows the integrand is absolutely continuous w.r.t. Lebesgue measure.
Provides a foundation for further analysis of measure-valued equations.
Abstract
In this paper Clark-Ocone representation for solution to measure-valued equation with interaction is studied. It is proven that the integrand is absolutely continuous with respect to Lebesgue measure.
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Taxonomy
TopicsStability and Controllability of Differential Equations