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The solution to the Fokker-Planck equation can be thought of as a macroscopic description of the dynamics of a diffusion process. Various results make this heuristic more precise - Ito integration, the Feynman-Kac theorem and so on. Do reaction-diffusion equations have a similar probabilistic interpretation? If so, where can I read about this? Many thanks. |
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Many reaction–diffusion systems can be interpreted as deterministic scaling limits of interacting particle systems, obtained in much the same way as the Fokker–Planck equation is obtained from a random walk (effectively a non-interacting particle system). Indeed, I would say that this is the reason why reaction–diffusion equations are useful for modelling real world systems involving, at a fundamental level, stochastic interactions of discrete entities. |
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