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Markov Processes with Identical Bridges

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Markov Processes with Identical Bridges
2.	Creator	Author's name, affiliation, country	P. J. Fitzsimmons; University of California, San Diego
3.	Subject	Discipline(s)	Mathematics
3.	Subject	Keyword(s)	Bridge law, eigenfunction, transition density.
3.	Subject	Subject classification	Primary: 60J25; secondary 60J35.
4.	Description	Abstract	Let $X$ and $Y$ be time-homogeneous Markov processes with common state space $E$, and assume that the transition kernels of $X$ and $Y$ admit densities with respect to suitable reference measures. We show that if there is a time $t>0$ such that, for each $x\in E$, the conditional distribution of $(X_s)_{0\le s\le t}$, given $X_0=x=X_t$, coincides with the conditional distribution of $(Y_s)_{0\le s\le t}$, given $Y_0=x=Y_t$, then the infinitesimal generators of $X$ and $Y$ are related by $L^Yf=\psi^{-1}L^X(\psi f)-\lambda f$, where $\psi$ is an eigenfunction of $L^X$ with eigenvalue $\lambda\in{\bf R}$. Under an additional continuity hypothesis, the same conclusion obtains assuming merely that $X$ and $Y$ share a "bridge" law for one triple $(x,t,y)$. Our work extends and clarifies a recent result of I. Benjamini and S. Lee.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	1998-07-05
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/34
10.	Identifier	Digital Object Identifier	10.1214/EJP.v3-34
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 3
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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