Recurrence criteria for generalized Dirichlet forms
| Autor: | Gerald Trutnau, Minjung Gim |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
Statistics and Probability
Pure mathematics Dirichlet form General Mathematics Existential quantification Probability (math.PR) 010102 general mathematics Probabilistic logic Perturbation (astronomy) Muckenhoupt weights Mathematics::Spectral Theory 01 natural sciences Dirichlet distribution 010104 statistics & probability symbols.namesake Norm (mathematics) FOS: Mathematics symbols 0101 mathematics Statistics Probability and Uncertainty primary: 31C25 47D07 60G17 secondary: 60J60 47B44 60J35 Mathematics - Probability Counterexample Mathematics |
| Popis: | We develop sufficient analytic conditions for recurrence and transience of non-sectorial perturbations of possibly non-symmetric Dirichlet forms on a general state space. These form an important subclass of generalized Dirichlet forms which were introduced in \cite{St1}. In case there exists an associated process, we show how the analytic conditions imply recurrence and transience in the classical probabilistic sense. As an application, we consider a generalized Dirichlet form given on a closed or open subset of $\mathbb{R}^d$ which is given as a divergence free first order perturbation of a non-symmetric energy form. Then using volume growth conditions of the sectorial and non-sectorial first order part, we derive an explicit criterion for recurrence. Moreover, we present concrete examples with applications to Muckenhoupt weights and counterexamples. The counterexamples show that the non-sectorial case differs qualitatively from the symmetric or non-symmetric sectorial case. Namely, we make the observation that one of the main criteria for recurrence in these cases fails to be true for generalized Dirichlet forms. Revised version: in particular the whole Section 2.2 was revised as in all previous arXiv-versions it was by mistake the preliminary Section 2.2 before its final revision |
| Databáze: | OpenAIRE |
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