Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1155436 | Stochastic Processes and their Applications | 2016 | 29 Pages |
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 (Tâ,μ) for Tâ<â has the law of the original process starting at x at time s and conditioned to have law μ at time Tâ. We will consider two types of conditioning: (a) weak conditioning when μ is absolutely continuous with respect to Ps,t(x,â
) and (b) strong conditioning when μ=εz for some zâE. 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Umut Ãetin, Albina Danilova,