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{1176991775,
author = {Mazziotto, G.},
title = {Two-Parameter Hunt Processes and a Potential Theory},
journal = {Ann. Probab.},
volume = {16},
number = {4},
year = {1988},
pages = { 600-619},
language = {en},
url = {http://dml.mathdoc.fr/item/1176991775}
}
Mazziotto, G. Two-Parameter Hunt Processes and a Potential Theory. Ann. Probab., Tome 16 (1988) no. 4, pp. 600-619. http://gdmltest.u-ga.fr/item/1176991775/