Evanescent and immobilized two-dimensional continuous-time random walks with exponential waiting-time distributions

Abstract

We derive expressions for the occupation probability density, characteristic function, and moments of two types of mortal random walks, namely evanescent and immobilized continuous-time random walks. Two types of evanescence or immobilization are considered: when evanescence or immobilization can only occur concurrently with a jump, and when evanescence or immobilization can occur any time. Compact expressions for the characteristic function are obtained for the special case where of exponential evanescence or immobility, and exponential waiting time distribution.