Blanchet, J;
Ruf, J;
(2016)
A weak convergence criterion for constructing changes of measure.
Stochastic Models
, 32
(2)
pp. 233-252.
10.1080/15326349.2015.1114891.
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Abstract
Based on a weak convergence argument, we provide a necessary and sufficient condition that guarantees that a nonnegative local martingale is indeed a martingale. Typically, conditions of this sort are expressed in terms of integrability conditions (such as the well-known Novikov condition). The weak convergence approach that we propose allows to replace integrability conditions by a suitable tightness condition. We then provide several applications of this approach ranging from simplified proofs of classical results to characterizations of processes conditioned on first passage time events and changes of measures for jump processes.
| Type: | Article |
|---|---|
| Title: | A weak convergence criterion for constructing changes of measure |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1080/15326349.2015.1114891 |
| Publisher version: | http://dx.doi.org/10.1080/15326349.2015.1114891 |
| Language: | English |
| Additional information: | © 2016 Taylor & Francis. This is an Accepted Manuscript of an article published by Taylor & Francis in Stochastic Models on 22 December 2015, available online: http://www.tandfonline.com/10.1080/15326349.2015.1114891 |
| Keywords: | Conditional queuing process, existence of weak solution, Girsanov theorem, local martingale, tightness |
| 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/1471920 |
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