Stochastic Processes, Infinitesimal Generators and Function Theory
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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].
KeywordsBrownian Motion Harmonic Function Markov Process Harmonic Measure Exit Time
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- J. P. Conway and J. J. Dudziak: Removable singularities for HP functions. Preprint 1984.Google Scholar
- L. Csink and B. Øksendal: A stochastic characterization of harmonic spaces. (To appear).Google Scholar
- B. Fuglede: Value distribution of harmonic and finely harmonic morphisms and applications in complex analysis. Köbenhavns Universitet Matematisk Institut Preprint Series 10 (1984).Google Scholar
- B. Øksendal: Finely harmonic functions with finite Dirichlet integral with respect to the Green measure. To appear in Trans. Amer. Math. Soc.Google Scholar
- B. Øksendal: An Introduction to Stochastic Differential Equations with Applications. (To appear on Springer-Verlag).Google Scholar
- В. Øksendal and A. Stray: Removable singularities for analytic functions with bounded Dirichlet integral. (To appear).Google Scholar