Ruf, J;
(2016)
Distribution of the time to explosion for one-dimensional diffusions.
Probability Theory and Related Fields
, 164
(3)
pp. 1027-1069.
10.1007/s00440-015-0625-9.
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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.
| Type: | Article |
|---|---|
| Title: | Distribution of the time to explosion for one-dimensional diffusions |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s00440-015-0625-9 |
| Publisher version: | http://dx.doi.org/10.1007/s00440-015-0625-9 |
| Language: | English |
| Additional information: | The final publication is available at Springer via http://dx.doi.org/10.1007/s00440-015-0625-9. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1463978 |
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