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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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. |
| Library of Congress subject classification: | Q Science > QA Mathematics |
| Sets: | Departments > Mathematics Departments > Statistics |
| Date Deposited: | 28 Sep 2015 09:46 |
| URL: | http://eprints.lse.ac.uk/63779/ |
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