Open Access
Translator Disclaimer
August, 1983 Harmonic Functions and the Dirichlet Problem for Revival Markov Processes
Kyle Siegrist
Ann. Probab. 11(3): 624-634 (August, 1983). DOI: 10.1214/aop/1176993506


Harmonic functions and the Dirichlet problem on an open set $G$ are defined for a pieced-out or revival Markov process constructed from a continuous base process. A one-to-one correspondence is obtained between the bounded harmonic functions of the revival process and those of the base process. The harmonic functions of the revival process are shown to be continuous on $G$ under certain conditions and to coincide with the solutions of $\mathscr{U}f = 0$ on $G$ where $\mathscr{U}$ is the characteristic operator. These results are applied to random evolution processes and branching processes.


Download Citation

Kyle Siegrist. "Harmonic Functions and the Dirichlet Problem for Revival Markov Processes." Ann. Probab. 11 (3) 624 - 634, August, 1983.


Published: August, 1983
First available in Project Euclid: 19 April 2007

zbMATH: 0516.60086
MathSciNet: MR704548
Digital Object Identifier: 10.1214/aop/1176993506

Primary: 60J45
Secondary: 60J25 , 60J80

Keywords: branching process , characteristic operator , Dirichlet problem , Harmonic function , Markov process , random evolution , revival process

Rights: Copyright © 1983 Institute of Mathematical Statistics


Vol.11 • No. 3 • August, 1983
Back to Top