Çetin, Umut 
ORCID: 0000-0001-8905-853X and Danilova, Albina
(2016)
Markov bridges: SDE representation.
Stochastic Processes and Their Applications, 126 (3).
651 - 679.
ISSN 0304-4149
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Abstract
Let X be a Markov process taking values in E with continuous paths and transition function (Ps,t).Given a measureμon(E,E), a Markov bridge starting at(s,εx)and ending at (T∗,μ) for T∗<∞ has the law of the original process starting at x at times and conditioned to have law μ at time T∗. We will consider two types of conditioning: (a)weak conditioning when μ is absolutely continuous with respect to Ps,t(x,·)and (b)strong conditioning when μ=εz for some z∈E. The main result of this paper is the representation of a Markov bridge as a solution to a stochastic differential equation (SDE) driven by a Brownian motion in a diffusion setting. Under mild conditions on the transition density of the underlying diffusion process we establish the existence and uniqueness of weak and strong solutions of this SDE
| Item Type: | Article |
|---|---|
| Official URL: | http://www.journals.elsevier.com/stochastic-proces... |
| Additional Information: | © 2015 Elsevier B.V. |
| Divisions: | Mathematics Statistics |
| Subjects: | Q Science > QA Mathematics |
| Date Deposited: | 28 Sep 2015 09:46 |
| Last Modified: | 05 Apr 2024 18:36 |
| URI: | http://eprints.lse.ac.uk/id/eprint/63779 |
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