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2016 Boundary Harnack principle for the absolute value of a one-dimensional subordinate Brownian motion killed at 0
Vanja Wagner
Electron. Commun. Probab. 21: 1-12 (2016). DOI: 10.1214/16-ECP28

Abstract

We prove the Harnack inequality and boundary Harnack principle for the absolute value of a one-dimensional recurrent subordinate Brownian motion killed upon hitting 0, when 0 is regular for itself and the Laplace exponent of the subordinator satisfies certain global scaling conditions. Using the conditional gauge theorem for symmetric Hunt processes we prove that the Green function of this process killed outside of some interval $(a,b)$ is comparable to the Green function of the corresponding killed subordinate Brownian motion. We also consider several properties of the compensated resolvent kernel $h$, which is harmonic for our process on $(0,\infty )$.

Citation

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Vanja Wagner. "Boundary Harnack principle for the absolute value of a one-dimensional subordinate Brownian motion killed at 0." Electron. Commun. Probab. 21 1 - 12, 2016. https://doi.org/10.1214/16-ECP28

Information

Received: 1 July 2016; Accepted: 9 November 2016; Published: 2016
First available in Project Euclid: 14 December 2016

zbMATH: 1354.60088
MathSciNet: MR3592206
Digital Object Identifier: 10.1214/16-ECP28

Subjects:
Primary: 60G51, 60J45, 60J57

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