## The Annals of Probability

### Two-Parameter Hunt Processes and a Potential Theory

G. Mazziotto

#### Abstract

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.

#### Article information

Source
Ann. Probab., Volume 16, Number 2 (1988), 600-619.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176991775

Digital Object Identifier
doi:10.1214/aop/1176991775

Mathematical Reviews number (MathSciNet)
MR929065

Zentralblatt MATH identifier
0681.60071

JSTOR