TY - JOUR
T1 - Parabolic Harnack inequality and heat kernel estimates for random walks with long range jumps
AU - Barlow, Martin T.
AU - Bass, Richard F.
AU - Kumagai, Takashi
N1 - Funding Information:
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).
PY - 2009/2
Y1 - 2009/2
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=56349111455&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=56349111455&partnerID=8YFLogxK
U2 - 10.1007/s00209-008-0326-5
DO - 10.1007/s00209-008-0326-5
M3 - Article
AN - SCOPUS:56349111455
SN - 0025-5874
VL - 261
SP - 297
EP - 320
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
IS - 2
ER -