Bernoulli

  • Bernoulli
  • Volume 5, Number 4 (1999), 589-614.

Scale-invariant diffusions: transience and non-polar points

Richard Dante Deblassie

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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).

Article information

Source
Bernoulli, Volume 5, Number 4 (1999), 589-614.

Dates
First available in Project Euclid: 19 February 2007

Permanent link to this document
https://projecteuclid.org/euclid.bj/1171899319

Mathematical Reviews number (MathSciNet)
MR1704557

Zentralblatt MATH identifier
0943.60079

Keywords
invariant measure martingale problem recurrence scale-invariant diffusions transience

Citation

Dante Deblassie, Richard. Scale-invariant diffusions: transience and non-polar points. Bernoulli 5 (1999), no. 4, 589--614. https://projecteuclid.org/euclid.bj/1171899319


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References

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