Une topologie fine associée au produit de deux processus markoviens
Let \(X^ 1\) and \(X^ 2\) be independent Markov processes on locally compact metric state spaces \(E^ 1\) and \(E^ 2\) respectively; assume they have strong Feller resolvents. These can be combined into a two parameter bi-Markov process: \(X_{st}=(X^ 1_ s,X^ 2_ t)\). A positive Borel measurable function f on \(E=E^ 1\times E^ 2\) is p- biexcessive if for all x in \(E^ 1\) and y in \(E^ 2\), both f(.,y) and f(x,.) are p-excessive. The authors define a fine topology in terms of hitting probabilities of the process \(X_{st}\). Their main result is that this topology is exactly the coarsest topology making all p- excessive functions continuous.
scientific article; zbMATH DE number 3888647