Gapeev, Pavel V. and Jeanblanc, Monique (2024) On the construction of conditional probability densities in the Brownian and compound Poisson filtrations. ESAIM: Probability and Statistics, 28. 62 - 74. ISSN 1292-8100
![]() |
Text (Gapeev_on-the-construction-of-conditional--published)
- Published Version
Available under License Creative Commons Attribution. Download (512kB) |
Abstract
In this paper, we construct supermartingales valued in [0,1] as solutions of an appropriate stochastic differential equation on a given reference filtration generated by either a Brownian motion or a compound Poisson process. Then, by means of the results contained in [M. Jeanblanc and S. Song, Stochastic Processes Appl. 121 (2011) 1389–1410], it is possible to construct an associated random time on some extended probability space admitting such a given supermartingale as conditional survival process and we shall check that this construction (with a particular choice of supermartingale) implies that Jacod’s equivalence hypothesis, that is, the existence of a family of strictly positive conditional probability densities for the random times with respect to the reference filtration, is satisfied. We use the components of the multiplicative decomposition of the constructed supermartingales to provide explicit expressions for the conditional probability densities of the random times on the Brownian and compound Poisson filtrations.
Item Type: | Article |
---|---|
Official URL: | https://www.esaim-ps.org/ |
Additional Information: | © 2024 The Authors |
Divisions: | Mathematics |
Subjects: | H Social Sciences > HA Statistics Q Science > QA Mathematics |
Date Deposited: | 14 Dec 2023 16:57 |
Last Modified: | 15 Aug 2024 19:16 |
URI: | http://eprints.lse.ac.uk/id/eprint/121059 |
Actions (login required)
![]() |
View Item |