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April, 1988 Two-Parameter Hunt Processes and a Potential Theory
G. Mazziotto
Ann. Probab. 16(2): 600-619 (April, 1988). DOI: 10.1214/aop/1176991775


A two-parameter Markov process $X$ with regular trajectories is associated to a pair of commuting Feller semigroups $P^1$ and $P^2$ considered on the same space $E$. A subsequent potential theory is developed with respect to an operator $\mathscr{L}$ which is the product of the generators of $P^1$ and $P^2$, respectively. The definition of a harmonic function $f$ on an open subset $A$ is expressed in terms of the hitting stopping line of $A^c$ by $X$ and the stochastic measure generated by $f(X)$. A PDE problem in $A$ with boundary conditions on $A^c$ is studied.


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G. Mazziotto. "Two-Parameter Hunt Processes and a Potential Theory." Ann. Probab. 16 (2) 600 - 619, April, 1988.


Published: April, 1988
First available in Project Euclid: 19 April 2007

zbMATH: 0681.60071
MathSciNet: MR929065
Digital Object Identifier: 10.1214/aop/1176991775

Primary: 60J45
Secondary: 31C10

Keywords: Biharmonic functions , commuting semigroups , Probabilistic potential theory , Two-parameter Markov process

Rights: Copyright © 1988 Institute of Mathematical Statistics

Vol.16 • No. 2 • April, 1988
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