Title: Aging Feynman-Kac Equation
Author: Wanli Wang
Aging phenomena is found to naturally appear in our world. We focus on the aging of functional distribution of the particles performing anomalous diffusion. Based on the aging continuous time random walk, the corresponding forward and backward Feynman-Kac equations are derived. According to the aging Feynman-Kac equations, the distribution of the occupation time and the corresponding moments are discussed. Compared with weak aging case, the most striking results include: the coefficient of the second moment of the occupation time in the positive space is 1/2 and has no relation with the aging time and the parameter of power law waiting time. Furthermore, the asymptotic behaviors of the first passage time are also considered, which have different behaviors for weak aging and strong aging.