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august 1999 Scale-invariant diffusions: transience and non-polar points
Richard Dante Deblassie
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Bernoulli 5(4): 589-614 (august 1999).

Abstract

Consider a diffusion in Rd (d ≥2) whose generator has coefficients independent of the distance to the origin. Then there is a parameter α so that the origin is almost surely hit when α< 1 and almost surely not hit when α> 1. Moreover, the process is transient to for α> 1. We identify α in terms of the diffusion coefficients and a certain invariant measure. In some special two-dimensional cases we explicitly compute the invariant measure and resolve the critical case α= 1. This work complements and extends certain results of Pinsky (1995) and Williams (1985).

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Richard Dante Deblassie. "Scale-invariant diffusions: transience and non-polar points." Bernoulli 5 (4) 589 - 614, august 1999.

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Published: august 1999
First available in Project Euclid: 19 February 2007

zbMATH: 0943.60079
MathSciNet: MR1704557

Keywords: invariant measure , Martingale problem , recurrence , scale-invariant diffusions , transience

Rights: Copyright © 1999 Bernoulli Society for Mathematical Statistics and Probability

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Vol.5 • No. 4 • august 1999
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