Numerical Algorithms for the Forward and Backward Fractional Feynman-Kac Equations

@article{Deng2015NumericalAF,
title={Numerical Algorithms for the Forward and Backward Fractional Feynman-Kac Equations},
author={Weihua Deng and Minghua Chen and Eli Barkai},
journal={J. Sci. Comput.},
year={2015},
volume={62},
pages={718-746}
}

The Feynman–Kac equations are a type of partial differential equations describing the distribution of functionals of diffusive motion. The probability density function (PDF) of Brownian functionals satisfies the Feynman–Kac formula, being a Schrödinger equation in imaginary time. The functionals of non-Brownian motion, or anomalous diffusion, follow the fractional Feynman–Kac equation (Carmi et al. in J Stat Phys 141:1071–1092, 2010), where the fractional substantial derivative is involved… CONTINUE READING