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Generalized local and nonlocal master equations for some stochastic processes. (English) Zbl 1443.60052

Summary: 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 Fokker-Planck equations, models for Lévy 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.

MSC:

60G99 Stochastic processes
60G07 General theory of stochastic processes
60J35 Transition functions, generators and resolvents
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