Open Access
December, 1974 The Excessive Functions of a Continuous Time Markov Chain
Michael W. Chamberlain
Ann. Probab. 2(6): 1075-1089 (December, 1974). DOI: 10.1214/aop/1176996499


Boundary conditions in the form of equalities have been used by Feller, Dynkin, and others to characterize the range of the resolvent operator for certain continuous time Markov chains. Along similar lines Denzel, Kemeny, and Snell were able to establish a characterization and Riesz decomposition for the excessive functions of a more restricted class of Markov chains through the use of boundary conditions in the form of inequalities. The present paper sets out to clarify and build upon this work by reanalyzing these excessive functions in a more general setting. Here the boundary theory developed by Chung is brought to bear on the problem so that the results can be derived in canonical form for probabilistic interpretation.


Download Citation

Michael W. Chamberlain. "The Excessive Functions of a Continuous Time Markov Chain." Ann. Probab. 2 (6) 1075 - 1089, December, 1974.


Published: December, 1974
First available in Project Euclid: 19 April 2007

zbMATH: 0296.60042
MathSciNet: MR362515
Digital Object Identifier: 10.1214/aop/1176996499

Primary: 60J10
Secondary: 60G17 , 60J35 , 60J45 , 60J50

Keywords: boundray conditions , characterization of sticky atoms , Chung's boundary theory , continuous time Markov chain , excessive functions , Feller's normal derivative , minimal chain , recurrent boundary atoms , representations , Riesz decomposition

Rights: Copyright © 1974 Institute of Mathematical Statistics

Vol.2 • No. 6 • December, 1974
Back to Top