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Martingales and Limit Theorems for Stochastic Processes

  • R. Sh. Liptser
  • A. N. Shiryaev
Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 45)

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.

Keywords

Central Limit Theorem Weak Convergence Wiener Process Strict Sense Diffusion Approximation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer-Verlag Berlin Heidelberg 1998

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  • R. Sh. Liptser
  • A. N. Shiryaev

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