 Markov bridges: SDE representationUmut Çetin and Albina Danilova Stochastic Processes and their Applications, 2016, vol. 126, issue 3, 651-679 Abstract: Let X be a Markov process taking values in E with continuous paths and transition function (Ps,t). Given a measure μ on (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 time s 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. Keywords: Markov bridge; h-transform; Martingale problem; Weak convergence (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:126:y:2016:i:3:p:651-679 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spa.2015.09.015 Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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