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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.

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Yanxiang Zhao, Jiakou Wang, Yanping Ma, and Qiang Du. 2016. Generalized local and nonlocal master equations for some stochastic processes. Comput. Math. Appl. 71, 11 (June 2016), 2497–2512.

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