Markov bridges: SDE representation

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:126

Article

Cetin, Umut¹  Danilova, Albina² 

[1] London Sch Econ & Polit Sci, Dept Stat, 10 Houghton St, London WC2A 2AE, England

[2] London Sch Econ & Polit Sci, Dept Math, 10 Houghton St, London WC2A 2AE, England

关键词: Markov bridge;    h-transform;    Martingale problem;    Weak convergence;   

DOI  :  10.1016/j.spa.2015.09.015

来源: Elsevier

【 摘 要 】

Let X be a Markov process taking values in E with continuous paths and transition function (P-s,P-t). Given a measure it on (E, E), a Markov bridge starting at (s, epsilon(x)) and ending at (T*, mu) for T* < infinity has the law of the original process starting at x at time s and conditioned to have law mu at time T*. We will consider two types of conditioning: (a) weak conditioning when mu is absolutely continuous with respect to P-s,P-t (x, .) and (b) strong conditioning when mu = epsilon(z) for some z is an element of 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. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

Free