- On a Class of Markov Semigroups on Discrete Ultra-Metric Spaces doi link

Auteur(s): Bendikov Alexander, Grigor’yan Alexander, Pittet Christophe

(Article) Publié: Potential Analysis, vol. 37 p.125-169 (2012)

Ref HAL: hal-01305034_v1
DOI: 10.1007/s11118-011-9249-6
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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.