Mean exit time and escape probability for the anomalous processes with the tempered power-law waiting times

This paper discusses two deterministic quantities, mean first exit time and escape probability, for the anomalous processes having the tempered Levy stable waiting times with the tempering index mu > 0 and the stability index 0 < alpha <= 1. We derive the nonlocal elliptic partial differential equations (PDEs) governing the mean first exit time and escape probability. Based on the analysis of the derived PDEs, some interesting phenomena are observed. Copyright (C) EPLA, 2017