Abstract
In this paper, we get a criteria of weak Poincare inequality by some integrability of hitting times for jump processes. In fact, integrability of hitting times on a subset F of state space E implies that the taboo process restricted on $E\setminus F$ is decay, from which we get a weak Poincare inequality with absorbing (Dirichlet) boundary. Using it and a local Poincare inequality, we obtain a weak Poincare inequality by the decomposition method.
Highlights
1 Introduction and main results During the recent years, a lot of progress has been made in the understanding of functional inequalities and their links with the convergence rates of Markov processes
In Section, we prove that some integrability of hitting times on a subset of state space is sufficient for the WPID ( . )
We get a criterion of weak Poincaré inequality by integrability of hitting times and a local Poincaré inequality on a fixed subset for jump processes
Summary
We use some integrability of hitting times to get a type of weak Poincaré inequality for jump processes, which can be used to study the convergence rates for jump processes in the sense of Pt – π ∞→. Assume that a local Poincaré inequality restricted on F is satisfied for a reversible q-processes with q-pair (q(x), q(x, dy)). If there exist a decreasing function ξ : [ , ∞) → ( , ∞) such that ξ (t) → as t → ∞, Eμξ (τF )– =: c < ∞, and MF := supx∈F q(x, Fc) < ∞, we have the weak Poincaré inequality In this theorem, we get a criterion of weak Poincaré inequality by integrability of hitting times and a local Poincaré inequality on a fixed subset for jump processes.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
