Döring, L;
Watson, AR;
Weissmann, P;
(2019)
Lévy processes with finite variance conditioned to avoid an interval.
Electronic Journal of Probability
, 24
(55)
pp. 1-32.
10.1214/19-EJP306.
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Abstract
Conditioning Markov processes to avoid a set is a classical problem that has been studied in many settings. In the present article we study the question if a Lévy process can be conditioned to avoid an interval and, if so, the path behavior of the conditioned process. For Lévy processes with finite second moments we show that conditioning is possible and identify the conditioned process as an h -transform of the original killed process. The h-transform is explicit in terms of successive overshoot distributions and is used to prove that the conditioned process diverges to + \infty and -\infty with positive probabilities.
| Type: | Article |
|---|---|
| Title: | Lévy processes with finite variance conditioned to avoid an interval |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1214/19-EJP306 |
| Publisher version: | http://dx.doi.org/10.1214/19-EJP306 |
| Language: | English |
| Additional information: | © The Authors. Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/). |
| Keywords: | Markov processes, Lévy processes, killed Lévy processes, Doob h-transform, martingales |
| 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 UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10079241 |
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