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July, 1987 Recurrence, Transience and Bounded Harmonic Functions for Diffusions in the Plane
Ross G. Pinsky
Ann. Probab. 15(3): 954-984 (July, 1987). DOI: 10.1214/aop/1176992075


We give conditions for transience and recurrence for certain diffusion processes in the plane which "look" recurrent in certain sectors and transient in others. We also give conditions for the convergence of diffusion paths to paths of the deterministic dynamical system corresponding to the first-order part of $L$, the generator of the process. This in turn is related to the question of existence of bounded harmonic functions for the operator $L$. Conditions are given for the existence and nonexistence of bounded harmonic functions for $L$.


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Ross G. Pinsky. "Recurrence, Transience and Bounded Harmonic Functions for Diffusions in the Plane." Ann. Probab. 15 (3) 954 - 984, July, 1987.


Published: July, 1987
First available in Project Euclid: 19 April 2007

zbMATH: 0625.60092
MathSciNet: MR893908
Digital Object Identifier: 10.1214/aop/1176992075

Primary: 60J60

Keywords: bounded harmonic functions , Diffusion processes , invariant $\sigma$-field , transience and recurrence

Rights: Copyright © 1987 Institute of Mathematical Statistics


Vol.15 • No. 3 • July, 1987
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