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

References

Publications referenced by this paper.
Showing 1-10 of 32 references

Numerical inversion of Laplace transforms of probability distributions

J. Abate
ORSA J. Comput. 7, 36–43 • 1995
View 4 Excerpts
Highly Influenced

On distributions of functionals of anomalous diffusion paths

S. Carmi, L. Turgeman, E. Barkai
J. Stat. Phys. 141, 1071–1092 • 2010
View 4 Excerpts
Highly Influenced

Fourth order difference approximations for space Riemann–Liouville derivatives based on weighted and shifted Lubich difference operators

M. H. Chen, W. H. Deng
Commun. Comput. Phys. • 2014

A numerical method for the fractional Fitzhugh–Nagumo monodomain model

F. Liu, I. Turner, V. Anh, Q. Yang, K. Burrage
ANZIAM J. 54, C608–C629 • 2013
View 1 Excerpt

Superlinearly convergent algorithms for the two-dimensional space– time Caputo–Riesz fractional diffusion equation

M. H. Chen, W. H. Deng, Y. J. Wu
Appl. Numer. Math. 70, 22–41 • 2013
View 1 Excerpt

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