Some inequalities related to transience and recurrence of Markov processes and their applications
Using the technique of Dirichlet forms, the author obtained a new conditions of transience and recurrence of irreducible \(m\)-symmetric Markov process on a locally compact separable metric space. The author identifies the connection these conditions with Harris recurrent too. The proved evolutions are applied to investigation of transient and recurrent of closed sets \(F\) relative to special constructed diffusion processes. The sufficient conditions are formulated in regard to complement of sets \(F\). The effectiveness of the proved criterions are confirmed by examples for a symmetric Markov processes on compact Riemannian manifolds.
scientific article; zbMATH DE number 5700613