Feynman-Kac theorems for generalized diffusions
Erik Ekstr\"om, Svante Janson, Johan Tysk
TL;DR
This paper extends Feynman-Kac theorems to generalized diffusions by establishing existence, uniqueness, and regularity results for equations with measure-valued coefficients, enabling new probabilistic representations.
Contribution
It introduces Feynman-Kac type theorems for generalized diffusions and proves foundational results for equations with measure-valued coefficients.
Findings
Established existence and uniqueness for measure-valued coefficient equations
Proved regularity results for generalized diffusion equations
Extended Feynman-Kac representations to broader diffusion classes
Abstract
We find Feynman-Kac type representation theorems for generalized diffusions. To do this we need to establish existence, uniqueness and regularity results for equations with measure-valued coefficients.
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Taxonomy
Topicsadvanced mathematical theories · Stochastic processes and financial applications · Stability and Controllability of Differential Equations