Local time of Levy random walks: a path integral approach

Abstract

Local time of a stochastic process quantifies the amount of time that sample trajectories $x(\tau )$ spend in the vicinity of an arbitrary point $x$. For a generic Hamiltonian, we employ the phase-space path-integral representation of random walk transition probabilities in order to quantify the properties of the local time. For time-independent systems, the resolvent of the Hamiltonian operator proves to be a central tool for this purpose. In particular, we focus on local times of Levy random walks (or Levy flights), which correspond to fractional diffusion equations.

10 pages

References in corpus (2)

• Green function of the double fractional Fokker-Planck equation: Path integral and stochastic differential equations
• Local-time representation of path integrals

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