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Markov bridges: SDE representation

Çetin, Umut and Danilova, Albina (2016) Markov bridges: SDE representation. Stochastic Processes and Their Applications, 126 (3). 651 - 679. ISSN 0304-4149

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Identification Number: 10.1016/j.spa.2015.09.015

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: 20 Aug 2021 00:59
URI: http://eprints.lse.ac.uk/id/eprint/63779

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