%0 Journal Article
%T On a Class of Markov Semigroups on Discrete Ultra-Metric Spaces
%+ Mathematical Institute, University of Wroclaw
%+ Universität Bielefeld = Bielefeld University
%+ Laboratoire d'Analyse, Topologie, Probabilités (LATP)
%A Bendikov, Alexander
%A Grigor’yan, Alexander
%A Pittet, Christophe
%Z Alexander Bendikov was supported by the Polish Government Scientific Research Fund, Grant No. N201 371736. Alexander Grigor’yan was supported by SFB 701 of German Research Council. Christophe Pittet was supported by the CNRS.
%< avec comité de lecture
%@ 0926-2601
%J Potential Analysis
%I Springer Verlag
%V 37
%N 2
%P 125-169
%8 2012-08
%D 2012
%R 10.1007/s11118-011-9249-6
%K Markov chain
%K Markov semigroup
%K Markov generator
%K ultra-metric space
%K heat kernel
%K transition probability
%Z 60J05; 60J27, 60J35, 60B15
%Z Mathematics [math]/Probability [math.PR]Journal articles
%X We consider a discrete ultra-metric space $\left( X,d\right) $ with a measure m and construct in a natural way a symmetric Markov semigroup $ \left\{ P_{t}\right\} _{t\geq 0}$ in $L^{2}\left( X,m\right) $ and the corresponding Markov process $\left\{ \mathcal{X}_{t}\right\} $ . We prove upper and lower bounds of its transition function and its Green function, give a criterion for the transience, and estimate its moments.
%G English
%L hal-01305034
%U https://hal.science/hal-01305034
%~ CNRS
%~ UNIV-AMU
%~ EC-MARSEILLE