منابع مشابه
Logarithmic Harnack inequalities∗
Logarithmic Sobolev inequalities first arose in the analysis of elliptic differential operators in infinite dimensions. Many developments and applications can be found in several survey papers [1, 9, 12]. Recently, Diaconis and Saloff-Coste [8] considered logarithmic Sobolev inequalities for Markov chains. The lower bounds for log-Sobolev constants can be used to improve convergence bounds for ...
متن کاملHarnack Inequalities in Infinite Dimensions
We consider the Harnack inequality for harmonic functions with respect to three types of infinite-dimensional operators. For the infinite dimensional Laplacian, we show no Harnack inequality is possible. We also show that the Harnack inequality fails for a large class of Ornstein-Uhlenbeck processes, although functions that are harmonic with respect to these processes do satisfy an a priori mod...
متن کاملHarnack Inequalities for Degenerate Diffusions
We study various probabilistic and analytical properties of a class of degenerate diffusion operators arising in Population Genetics, the so-called generalized Kimura diffusion operators [8, 9, 6]. Our main results are a stochastic representation of weak solutions to a degenerate parabolic equation with singular lower-order coefficients, and the proof of the scaleinvariant Harnack inequality fo...
متن کاملHarnack inequalities for jump processes
We consider a class of pure jump Markov processes in R whose jump kernels are comparable to those of symmetric stable processes. We establish a Harnack inequality for nonnegative functions that are harmonic with respect to these processes. We also establish regularity for the solutions to certain integral equations.
متن کاملStability of Parabolic Harnack Inequalities
Let (G,E) be a graph with weights {axy} for which a parabolic Harnack inequality holds with space-time scaling exponent β ≥ 2. Suppose {axy} is another set of weights that are comparable to {axy}. We prove that this parabolic Harnack inequality also holds for (G,E) with the weights {axy}. We also give stable necessary and sufficient conditions for this parabolic Harnack inequality to hold.
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ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 1996
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.1996.v3.n6.a8