Levy随机游动的局部时：路径积分方法
Local time of Levy random walks: a path integral approach
摘要：
随机过程的本地时间量化样本轨迹$x(τ)$在任意点$x$附近花费的时间量。对于一般的哈密顿量，我们采用相空间路径积分表示的随机行走转移概率，以量化的本地时间的属性。对于与时间无关的系统，哈密顿算子的预解式被证明是实现这一目的的核心工具。特别是，我们专注于当地时间的利维随机游动（或利维航班），这对应于分数阶扩散方程。
英文摘要：
Local time of a stochastic process quantifies the amount of time that sample trajectories $x(τ)$ 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.
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