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Homogeneous Random Measures and Strongly Supermedian Kernels of a Markov Process

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1.	Title	Title of document	Homogeneous Random Measures and Strongly Supermedian Kernels of a Markov Process
2.	Creator	Author's name, affiliation, country	Patrick J. Fitzsimmons; UCSD
2.	Creator	Author's name, affiliation, country	Ronald K. Getoor; UCSD
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Homogeneous random measure, additive functional, Kuznetsov measure, potential kernel, characteristic measure, strongly supermedian, smooth measure.
3.	Subject	Subject classification	Primary 60J55; secondary 60J45, 60J40
4.	Description	Abstract	The potential kernel of a positive left additive functional (of a strong Markov process $X$) maps positive functions to strongly supermedian functions and satisfies a variant of the classical domination principle of potential theory. Such a kernel $V$ is called a regular strongly supermedian kernel in recent work of L. Beznea and N. Boboc. We establish the converse: Every regular strongly supermedian kernel $V$ is the potential kernel of a random measure homogeneous on $[0,\infty[$. Under additional finiteness conditions such random measures give rise to left additive functionals. We investigate such random measures, their potential kernels, and their associated characteristic measures. Given a left additive functional $A$ (not necessarily continuous), we give an explicit construction of a simple Markov process $Z$ whose resolvent has initial kernel equal to the potential kernel $U_{\!A}$. The theory we develop is the probabilistic counterpart of the work of Beznea and Boboc. Our main tool is the Kuznetsov process associated with $X$ and a given excessive measure $m$.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2003-07-03
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/142
10.	Identifier	Digital Object Identifier	10.1214/EJP.v8-142
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 8
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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