Fractional Feynman-Kac Equation for Non-Brownian Functionals

Lior Turgeman, Shai Carmi, Eli Barkai

Research output: Contribution to journalArticlepeer-review

76 Scopus citations


We derive backward and forward fractional Feynman-Kac equations for the distribution of functionals of the path of a particle undergoing anomalous diffusion. Fractional substantial derivatives introduced by Friedrich and co-workers provide the correct fractional framework for the problem. For applications, we calculate the distribution of occupation times in half space and show how the statistics of anomalous functionals is related to weak ergodicity breaking.

Original languageEnglish
Article number190201
JournalPhysical Review Letters
Issue number19
StatePublished - 6 Nov 2009


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