Discussiones Mathematicae Probability and Statistics 22(1,2) (2002) 53-59

ESTIMATES FOR THE DISTRIBUTION OF THE FIRST EXIT TIME OF α-STABLE PROCESSES

Wiesław Cupała

Institute of Mathematics
University of Zielona Góra
Podgórna, 50 65-246 Zielona Góra, Poland
e-mail: w.cupala@im.uz.zgora.pl

Abstract

The Varopoulos-Hardy-Littlewood theory and the spectral analysis are used to estimate the tail of the distribution of the first exit time of α-stable processes. 

Keywords: first exit time, α-stable processes.

2000 Mathematics Subject Classification: 60G40, 60J25.

References

[1]
D. Levin and M. Solomyak, Rozenblum-Lieb-Cwikel inequality for Markov generators, J. d'Anal. Math. 71 (1997), 173-193.
[2]
N.T. Varopoulos, Hardy-Littlewood theory for semigroups, J. Funct. Anal. 63 (1985), 240-260.

Received 25 October 2002