Weak Poincaré inequalities and L-2-convergence rates of Markov semigroups

Röckner M, Wang F-Y (2001)
Journal of Functional Analysis 185(2): 564-603.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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Abstract / Bemerkung
In order to describe L-2-convergence rates slower than exponential. the weak Poincare inequality is introduced. It is shown that the convergence rate of a Markov semigroup and the corresponding weak Poincare inequality can be determined by each other. Conditions for the weak Poincare inequality to hold are presented, which are easy to check and which hold in many applications. The weak Poincare inequality is also studied by using isoperimetric inequalities for diffusion and jump processes. Some typical examples are given to illustrate the general results. In particular, our results are applied to the stochastic quantization of field theory in finite Volume. Moreover, a sharp criterion of weak Poincare inequalities is presented for Poisson measures on configuration spaces. (C) 2001 Academic Press.
Erscheinungsjahr
Zeitschriftentitel
Journal of Functional Analysis
Band
185
Ausgabe
2
Seite(n)
564-603
ISSN
PUB-ID

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Röckner M, Wang F-Y. Weak Poincaré inequalities and L-2-convergence rates of Markov semigroups. Journal of Functional Analysis. 2001;185(2):564-603.
Röckner, M., & Wang, F. - Y. (2001). Weak Poincaré inequalities and L-2-convergence rates of Markov semigroups. Journal of Functional Analysis, 185(2), 564-603. doi:10.1006/jfan.2001.3776
Röckner, M., and Wang, F. - Y. (2001). Weak Poincaré inequalities and L-2-convergence rates of Markov semigroups. Journal of Functional Analysis 185, 564-603.
Röckner, M., & Wang, F.-Y., 2001. Weak Poincaré inequalities and L-2-convergence rates of Markov semigroups. Journal of Functional Analysis, 185(2), p 564-603.
M. Röckner and F.-Y. Wang, “Weak Poincaré inequalities and L-2-convergence rates of Markov semigroups”, Journal of Functional Analysis, vol. 185, 2001, pp. 564-603.
Röckner, M., Wang, F.-Y.: Weak Poincaré inequalities and L-2-convergence rates of Markov semigroups. Journal of Functional Analysis. 185, 564-603 (2001).
Röckner, Michael, and Wang, Feng-Yu. “Weak Poincaré inequalities and L-2-convergence rates of Markov semigroups”. Journal of Functional Analysis 185.2 (2001): 564-603.