Generalized local and nonlocal master equations for some stochastic processes ?
In this paper, we present a study on generalized local and nonlocal equations for some stochastic processes. By considering the net flux change in a region determined by the transition probability, we derive the master equation to describe the evolution of the probability density function. Some examples, such as classical FokkerPlanck equations, models for Lvy process, and stochastic coagulation equations, are provided as illustrations. A particular application is a consistent derivation of coupled dynamical systems for spatially inhomogeneous stochastic coagulation processes.
stochastic coagulation nonlocal flux smoluchowski equation conservation law nonlocal diffusion fractional diffusion