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Stochastic Processes, Infinitesimal Generators and Function Theory

Chapter
Part of the NATO ASI series book series (ASIC, volume 153)

Abstract

It is now well known that there is a close connection between Brownian motion and (classical) harmonic functions. This discovery started with Kakutani’s solution in 1944 [22 ] of the Dirichlet problem by using Brownian motion. Subsequently many other striking connections have been found and they have been extended to general Markov processes and associated harmonic spaces. See e.g. Constantinescu & Cornea [ 5 ] and Bliedtner & Hansen [ 3].

Keywords

Brownian Motion Harmonic Function Markov Process Harmonic Measure Exit Time 
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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Copyright information

© D. Reidel Publishing Company 1985

Authors and Affiliations

  1. 1.Department of MathematicsCalifornia Institute of TechnologyPasadenaUSA

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