Abstract
We investigate the relationships between the parabolic Harnack inequality, heat kernel estimates, some geometric conditions, and some analytic conditions for random walks with long range jumps. Unlike the case of diffusion processes, the parabolic Harnack inequality does not, in general, imply the corresponding heat kernel estimates.
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M. T. Barlow’s research was partially supported by NSERC (Canada), the twenty-first century COE Program in Kyoto University (Japan), and by EPSRC (UK). R. F. Bass’s research was partially supported by NSF Grant DMS-0601783. T. Kumagai’s research was partially supported by the Grant-in-Aid for Scientific Research (B) 18340027 (Japan).
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Barlow, M.T., Bass, R.F. & Kumagai, T. Parabolic Harnack inequality and heat kernel estimates for random walks with long range jumps. Math. Z. 261, 297–320 (2009). https://doi.org/10.1007/s00209-008-0326-5
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DOI: https://doi.org/10.1007/s00209-008-0326-5