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Distribution of the time to explosion for one-dimensional diffusions

Karatzas, Ioannis and Ruf, Johannes (2015) Distribution of the time to explosion for one-dimensional diffusions. Probability Theory and Related Fields, 164 (3). pp. 1027-1069. ISSN 0178-8051

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Identification Number: 10.1007/s00440-015-0625-9

Abstract

We study the distribution of the time to explosion for one-dimensional diffusions. We relate this question to the computation of expectations of suitable nonnegative local martingales. Moreover, we characterize the distribution function of the time to explosion as the minimal solution to a certain Cauchy problem for an appropriate parabolic differential equation; this leads to alternative characterizations of Feller’s criterion for explosions. We discuss in detail several examples for which it is possible to obtain analytic expressions for the corresponding distribution of the time to explosion, using the methodologies developed in the paper

Item Type: Article
Official URL: https://link.springer.com/journal/440
Additional Information: © 2015 Springer
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Sets: Departments > Mathematics
Date Deposited: 11 Oct 2017 09:29
Last Modified: 30 Jan 2019 20:09
Projects: NSF-DMS-14-05210
Funders: National Science Foundation
URI: http://eprints.lse.ac.uk/id/eprint/84575

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