arXiv subjects

Ling-Di Wang

Publications and source records attributed to Ling-Di Wang.

4 recordsLinked to original sources

arXiv2025

Non-(strong, geometrically) ergodicity criteria for discrete time Markov chains on general state

For discrete-time Markov chains on general state spaces, we establish criteria for non-ergodicity and non-strong ergodicity, and derive sufficient conditions for non-geometric ergodicity via the theory of minimal nonnegative solutions. Our criteria are formulated based on the existence of solutions to inequalities involving the chain's one-step transition kernel. Meanwhile, these practical criteria are applied to a type of examples, which can effectively characterize the non-ergodicity and non-strong ergodicity of a specific class of single birth (death) processes.

math.PR↗

arXiv2015

Mixed Eigenvalues of {\LARGE $\pmb p$\,}-Laplacian

The mixed principal eigenvalue of $p\,$-Laplacian (equivalently, the optimal constant of weighted Hardy inequality in $L^p$ space) is studied in this paper. Several variational formulas for the eigenvalue are presented. As applications of the formulas, a criterion for the positivity of the eigenvalue is obtained. Furthermore, an approximating procedure and some explicit estimates are presented case by case. An example is included to illustrate the power of the results of the paper.

math.SP↗

arXiv2014

Mixed Eigenvalues of Discrete {\LARGE $\pmb p$\,}-Laplacian

This paper deals with the principal eigenvalue of discrete $p$-Laplacian on the set of nonnegative integers. Alternatively, it is studying the optimal constant of a class of weighted Hardy inequalities. The main goal is the quantitative estimates of the eigenvalue. The paper begins with the case having reflecting boundary at origin and absorbing boundary at infinity. Several variational formulas are presented in different formulation: the difference form, the single summation form and the double summation form. As their applications, some explicit lower and upper estimates, a criterion for positivity (which was known years ago), as well as an approximating procedure for the eigenvalue are obtained. Similarly, the dual case having absorbing boundary at origin and reflecting boundary at infinity is also studied. Two examples are presented at the end of Section 2 to illustrate the value of the investigation.

math.SP↗

arXiv2012

Mixed principal eigenvalues in dimension one

This is one of a series of papers exploring the stability speed of one-dimensional stochastic processes. The present paper emphasizes on the principal eigenvalues of elliptic operators. The eigenvalue is just the best constant in the $L^{2}$-Poincaré inequality and describes the decay rate of the corresponding diffusion process. We present some variational formulas for the mixed principal eigenvalues of the operators. As applications of these formulas, we obtain case by case explicit estimates, a criterion for positivity, and an approximating procedure for the eigenvalue.

math.PR↗