This paper develops precise estimates for the potential kernel, capacities of large intervals, and the probabilities of hitting large intervals for the asymmetric Cauchy processes. These are then applied to study three problems concerning the sample paths: (i) the rate of escape of $|X_t|$ as $t \rightarrow \infty$; (ii) the sizes of the large holes in the range of the process; (iii) the asymptotic behavior of the Lebesgue measure of that part of the range of the process that is in a large interval.
Publié le : 1983-05-14
Classification:
Potential theory,
hitting probabilities,
rate of escape,
holes in range,
Lebesgue measure of range,
60G17,
60J30
@article{1176993598,
author = {Pruitt, William E. and Taylor, S. James},
title = {The Behavior of Asymmetric Cauchy Processes for Large Time},
journal = {Ann. Probab.},
volume = {11},
number = {4},
year = {1983},
pages = { 302-327},
language = {en},
url = {http://dml.mathdoc.fr/item/1176993598}
}
Pruitt, William E.; Taylor, S. James. The Behavior of Asymmetric Cauchy Processes for Large Time. Ann. Probab., Tome 11 (1983) no. 4, pp. 302-327. http://gdmltest.u-ga.fr/item/1176993598/