Stochastic Functional Differential Equations and Feynman-Kac Formula

Stefano Belloni

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arXiv · 1602.08336

Stochastic Functional Differential Equations and Feynman-Kac Formula

Stefano Belloni

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Abstract

In the framework of stochastic functional differential equations (SFDE's) and the corresponding calculus developed in the recent years by F. Yan and S. Mohammed, we provide a series of representation formulae for a variety of highly degenerate functional differential equations of the type of the Feynman-Kac formulae. More precisely, we study the stochastic process satisfying regular SFDE's with killing and absorbing boundary, we give the differential equation to be solved in order to compute the distribution of the first exit time from a regular domain and apply our results to a model describing bacterial motility and to the derivation of a path-dependent Black-Scholes equation.

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Stefano Belloni. 2016-02-26. Stochastic Functional Differential Equations and Feynman-Kac Formula. https://arxiv.org/abs/1602.08336

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