Feynman-Kac Equations for Reaction and Diffusion Processes

Abstract

This paper provides a theoretical framework of deriving the forward and backward Feynman-Kac equations for the distribution of functionals of the path of a particle undergoing both diffusion and chemical reaction. Very general forms of the equations are obtained. Once given the diffusion type and reaction rate, a specific forward or backward Feynman-Kac equation can be obtained. The listed in the paper include the ones for normal/anomalous diffusions and reactions with linear/nonlinear rates. Using the derived equations, we also study the occupation time in half-space, the first passage time to a fixed boundary, and the occupation time in half-space with absorbing or reflecting boundary conditions.

arXiv comment15 pages, 4 figures

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Cited by in corpus (3)

• Feynman-Kac equation revisited
• Subdiffusion in the Presence of Reactive Boundaries: A Generalized Feynman-Kac Approach
• Numerical algorithms of the two-dimensional Feynman-Kac equation for reaction and diffusion processes