## The Annals of Probability

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

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

#### 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

**Permanent link to this document**

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**

links.jstor.org

**Subjects**

Primary: 60J45: Probabilistic potential theory [See also 31Cxx, 31D05]

Secondary: 31C10: Pluriharmonic and plurisubharmonic functions [See also 32U05]

**Keywords**

Two-parameter Markov process biharmonic functions commuting semigroups probabilistic potential theory

#### Citation

Mazziotto, G. Two-Parameter Hunt Processes and a Potential Theory. Ann. Probab. 16 (1988), no. 2, 600--619. doi:10.1214/aop/1176991775. https://projecteuclid.org/euclid.aop/1176991775