Symmetric markov chains on double-struck Z signd with unbounded range

Transactions of the American Mathematical Society

Volumn 360, Issue 4, 2008, Pages 2041-2075

  Bass, Richard F ^a   Kumagai, Takashi ^b  

^a UNIVERSITY OF CONNECTICUT   (United States)

^b KYOTO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 62549150143     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-07-04281-X     Document Type: Article

References (18)

1. D. Aldous. Stopping times and tightness, Ann. Probab., 6 (1978), 335-340. MR0474446 (57:14086)
2. M.T. Barlow, R.F. Bass and C. Gui, The Liouville property and conjecture of De Giorgi, Comm. Pure Appl. Math., 53 (2000), 1007-1038. MR1755949 (2001m:35095)
3. R.F. Bass and M. Kassmann, Harnack inequalities for non-local operators of variable order, Trans. Amer. Math. Soc. 357, (2005) 837-850. MR2095633 (2005i:60104)
4. R.F. Bass and D.A. Levin, Transition probabilities for symmetric jump processes, Trans. Amer. Math. Soc. 354, no. 7 (2002), 2933-2953. MR1895210 (2002m:60132)
5. R.F. Bass and D.A. Levin, Harnack inequalities for jump processes, Potential Anal. 17 (2002), 375-388. MR1918242 (2003e:60194)
6. P. Billingsley, Convergence of Probability Measures, 2nd ed., John Wiley, New York, 1999. MR1700749 (2000e:60008)
7. E.A. Carlen and S. Kusuoka and D.W. Stroock, Upper bounds for symmetric Markov transition functions, Ann. Inst. Henri Poincare-Probab. Statist. 23 (1987), 245-287. MR898496 (88i:35066)
8. Z.Q. Chen and T. Kumagai, Heat kernel estimates for stable-like processes on d-sets, Stochastic Process Appl. 108 (2003), 27-62. MR2008600 (2005d:60135)
9. M. Fukushima, Y. Oshima, and M. Takeda, Dirichlet Forms and Symmetric Markov Processes, deGruyter, Berlin, 1994. MR1303354 (96f:60126)
10. J. Hu and T. Kumagai, Nash-type inequalities and heat kernels for non-local Dirichlet forms, Kyushu J. Math. 60 (2006), 245-265. MR2268236
11. D. Jerison, The weighted Poincare inequality for vector fields satisfying Hormander's condition. Duke Math. J. 53 (1986), 503-523. MR850547 (87i:35027)
12. G.F. Lawler, Estimates for differences and Harnack inequality for difference operators coming from random walks with symmetric, spatially inhomogeneous, increments, Proc. London Math. Soc. 63 (1992), 552-568. MR1127149 (93a:60103)
13. G.F. Lawler and T.W. Polaski, Harnack inequalities and difference estimates for random walks with infinite range, J. Theor. Prob. 6 (1993) 781-802. MR1245395 (94i:60079)
14. T. Leviatan, Perturbations of Markov processes, J. Funct. Anal. 10 (1972), 309-325. MR0400409 (53:4243)
15. P.-A. Meyer, Renaissance, recollements, melanges, ralentissement de processus de Markov, Ann. Inst. Fourier 25 (1975), 464-497. MR0415784 (54:3862)
16. F. Spitzer, Principles of Random Walk, Springer-Verlag, New York, 1976. MR0388547 (52:9383)
17. D.W. Stroock and S.R.S. Varadhan, Multidimensional Diffusion Processes, Springer-Verlag, Berlin, 1979. MR532498 (81f:60108)
18. D.W. Stroock and W. Zheng, Markov chain approximations to symmetric diffusions, Ann. Inst. Henri. Poincare-Probab. Statist. 33 (1997), 619-649. MR1473568 (98k:60125) (Pubitemid 127168346)