Tohoku Mathematical Journal

Density estimate in small time for jump processes with singular Lévy measures

Yasushi Ishikawa

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Abstract

We consider the asymptotic behaviour of the transition density for processes of jump type as the time parameter $t$ tends to 0. We use Picard's duality method, which allows us to obtain the lower and upper bounds of the density even for the case where the support of Lévy measure is singular. The main result is that, under certain restrictions, the density behaves in polynomial order or may decrease in exponential order as $t\to0$ according to geometrical conditions of the objective points.

Article information

Source
Tohoku Math. J. (2) Volume 53, Number 2 (2001), 183-202.

Dates
First available in Project Euclid: 3 May 2007

Permanent link to this document
http://projecteuclid.org/euclid.tmj/1178207478

Digital Object Identifier
doi:10.2748/tmj/1178207478

Mathematical Reviews number (MathSciNet)
MR2002g:60124

Zentralblatt MATH identifier
1011.60064

Subjects
Primary: 60J75: Jump processes
Secondary: 60J25: Continuous-time Markov processes on general state spaces

Citation

Ishikawa, Yasushi. Density estimate in small time for jump processes with singular Lévy measures. Tohoku Math. J. (2) 53 (2001), no. 2, 183--202. doi:10.2748/tmj/1178207478. http://projecteuclid.org/euclid.tmj/1178207478.


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