Functionals of the path of a Brownian particle are known to obey the celebrated Feynman–Kac equation. We develop here a fractional Feynman–Kac equation for functionals of the sub–diffusive continuous-time random walk process. Several simple examples of functionals are explicitly treated such as the occupation time, the first passage time, and the maximum of the walk. In the presence of a binding field, the fractional Feynman–Kac equation describes the route to weak ergodicity breaking.
|Original language||American English|
|Title of host publication||Fractional Dynamics|
|Subtitle of host publication||Recent Advances|
|Publisher||World Scientific Publishing Co.|
|Number of pages||23|
|ISBN (Print)||9814340588, 9789814340588|
|State||Published - 1 Jan 2011|
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