Strong Feller continuity of Feller processes and semigroups (Q2909259)
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scientific article; zbMATH DE number 6074044
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Strong Feller continuity of Feller processes and semigroups |
scientific article; zbMATH DE number 6074044 |
Statements
30 August 2012
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strong Feller property
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locally uniform absolute continuity
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local Orlicz-ultracontractivity
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Feller processes
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harmonic functions
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first exit times
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Strong Feller continuity of Feller processes and semigroups (English)
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The authors study the strong Feller property for a Markov process and the the corresponding sub-Markov semigroup. The main goal is to establish two equivalent criteria for the strong Feller property: one is described by the local uniform absolute continuity of the transition probabilities \(\operatorname{P}_t(x,dy)\), while the other is based on local Orlicz-ultracontractivity. These two criteria generalize many existing results.NEWLINENEWLINEIn the last part of the paper, the authors consider Feller processes with the strong Feller property, establish estimates of the first exit times from balls, and investigate continuity of harmonic functions.
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