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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). pp. 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 measure � on (E; E ), a Markov bridge starting at (s; "x) and ending at (T�; �) for T� < 1 has the law of the original process starting at x at time s and conditioned to have law � at time T�. We will consider two types of conditioning: a) weak conditioning when � is absolutely continuous with respect to Ps;t(x; �) and b) strong conditioning when � = "z for some z 2 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
Sets: Departments > Mathematics
Departments > Statistics
Date Deposited: 28 Sep 2015 09:46
Last Modified: 20 Apr 2019 01:23
URI: http://eprints.lse.ac.uk/id/eprint/63779

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