Abstract
In contemporary probability theory, martingales are a wide class of processes to which such fundamental processes as Brownian motion and the centered Poisson process are related. If one pursues an analogy with mathematical physics and potential theory, then the concept corresponding to the martingale is the concept of the harmonic function. Related to the martingale are submartingales and supermartingales, and their corresponding concepts in analysis are subharmonic and superharmonic functions.
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