Heat kernel estimates for jump processes of mixed types on metric measure spaces View Full Text


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Article Info

DATE

2008-01

AUTHORS

Zhen-Qing Chen, Takashi Kumagai

ABSTRACT

In this paper, we investigate symmetric jump-type processes on a class of metric measure spaces with jumping intensities comparable to radially symmetric functions on the spaces. The class of metric measure spaces includes the Alfors d-regular sets, which is a class of fractal sets that contains geometrically self-similar sets. A typical example of our jump-type processes is the symmetric jump process with jumping intensity where ν is a probability measure on , c(α, x, y) is a jointly measurable function that is symmetric in (x, y) and is bounded between two positive constants, and c0(x, y) is a jointly measurable function that is symmetric in (x, y) and is bounded between γ1 and γ2, where either γ2 ≥ γ1 > 0 or γ1 = γ2 = 0. This example contains mixed symmetric stable processes on as well as mixed relativistic symmetric stable processes on . We establish parabolic Harnack principle and derive sharp two-sided heat kernel estimate for such jump-type processes. More... »

PAGES

277-317

References to SciGraph publications

  • 2002-12. Harnack Inequalities for Jump Processes in POTENTIAL ANALYSIS
  • 2004-01. Harnack inequality for some classes of Markov processes in MATHEMATISCHE ZEITSCHRIFT
  • 2005-03. Harnack’s Inequality for Stable Lévy Processes in POTENTIAL ANALYSIS
  • 1992-06. On reflected Dirichlet spaces in PROBABILITY THEORY AND RELATED FIELDS
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    http://scigraph.springernature.com/pub.10.1007/s00440-007-0070-5

    DOI

    http://dx.doi.org/10.1007/s00440-007-0070-5

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