Upper Bounds for symmetric Markov transition functions

E. A. Carlen; S. Kusuoka; D. W. Stroock

Annales de l'I.H.P. Probabilités et statistiques (1987)

  • Volume: 23, Issue: S2, page 245-287
  • ISSN: 0246-0203

How to cite

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Carlen, E. A., Kusuoka, S., and Stroock, D. W.. "Upper Bounds for symmetric Markov transition functions." Annales de l'I.H.P. Probabilités et statistiques 23.S2 (1987): 245-287. <http://eudml.org/doc/77309>.

@article{Carlen1987,
author = {Carlen, E. A., Kusuoka, S., Stroock, D. W.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {locally compact separable metric space; strongly continuous semigroup; Nash-type inequalities; Sobolev-type inequality},
language = {eng},
number = {S2},
pages = {245-287},
publisher = {Gauthier-Villars},
title = {Upper Bounds for symmetric Markov transition functions},
url = {http://eudml.org/doc/77309},
volume = {23},
year = {1987},
}

TY - JOUR
AU - Carlen, E. A.
AU - Kusuoka, S.
AU - Stroock, D. W.
TI - Upper Bounds for symmetric Markov transition functions
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1987
PB - Gauthier-Villars
VL - 23
IS - S2
SP - 245
EP - 287
LA - eng
KW - locally compact separable metric space; strongly continuous semigroup; Nash-type inequalities; Sobolev-type inequality
UR - http://eudml.org/doc/77309
ER -

References

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  1. [B-E] D. Bakry and M. Emery, Diffusions Hypercontractives, pp. 177-207 in Sem. de Probabilities XIX; Lecture Notes in Mathematics, # 1123, J. AZEMA and M. YOR Eds., Springer-Verlag, New York, 1985. Zbl0561.60080MR889476
  2. [D] E.B. Davies, Explicit Constants for the Gaussian Upper Bounds on Heat Kernels, 1985 preprint (to appear). 
  3. [D-M] C. Dellacherie and P.A. Meyer, Probabilities and Potential B, North Holland, Amsterdam, 1982. Zbl0494.60002MR745449
  4. [F-S] E.B. Fabes and D.W. Stroock, A New Proof of Moser's Parabolic Harnack Inequality Via the Old Ideas of Nash, Arch. Ratl. Mech. and Anal., vol. 96#4, pp. 327-338 ( 1986). Zbl0652.35052MR855753
  5. [F] M. Fukushima, Dirichlet Forms and Markov Processes, North Holland, Amsterdam, 1980. Zbl0422.31007MR569058
  6. [K-S] S. Kusuoka and D. Stroock, Long time estimates for the heat kernel assiciated will a uniformly subelliptic symmetric second order operator, to appear in Ann. Math. Zbl0699.35025MR924675
  7. [N] J. Nash, Continuity of Solutions of Parabolic and Elliptic Equations, Amer. J. Math., Vol. 80, 1958, pp. 931-954. Zbl0096.06902MR100158
  8. [S] I.E. Segal, Construction of Nonlinear Local Quantum Processes: I, Ann. Math., Vol. 92, 1970, pp. 462-481. Zbl0213.40904MR272306
  9. [St] D.W. Stroock, Applications of Fefferman-Stein Type Interpolation to Probability and Analysis, Comm. Pure Appl. Math., Vol. XXVI, 1973, pp. 477-496. Zbl0267.60051MR341601
  10. [L. D.] D.W. Stroock, An Introduction to the Theory of Large Deviations, Springer-Verlag, New York, 1984. Zbl0552.60022MR755154
  11. [V] S.R.S. Varadhan, On the Behavior of the Fundamental Solution of the Heat Equation with Variable Coefficients, C.A.M.S. 20 # 2, pp. 431-455, 1967. Zbl0155.16503MR208191
  12. [V-1] N.Th. Varopoulos, Isoperimetric Inequalities and Markov Chains, J. Func. Anal., Vol. 63, 1985, pp. 215-239. Zbl0573.60059MR803093
  13. [V-2] N.Th. Varopoulos, Hardy-Littlewood Theory for Semigroups, J. Func. Anal., Vol. 63, 1985, pp. 240-260. Zbl0608.47047MR803094

Citations in EuDML Documents

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  1. Dominique Bakry, Dominique Michel, Inégalités de Sobolev et minorations du semi-groupe de la chaleur
  2. Martin Barlow, Harmonic analysis on fractal spaces
  3. D. Bakry, D. Concordet, M. Ledoux, Optimal heat kernel bounds under logarithmic Sobolev inequalities
  4. M. D. Jara, C. Landim, Quenched non-equilibrium central limit theorem for a tagged particle in the exclusion process with bond disorder
  5. Jean-Christophe Mourrat, Scaling limit of the random walk among random traps on ℤd
  6. Dominique Bakry, Inégalités de Sobolev faibles : un critère Γ 2
  7. T. Delmotte, Inégalité de Harnack elliptique sur les graphes
  8. Jean-Dominique Deuschel, Holger Kösters, The quenched invariance principle for random walks in random environments admitting a bounded cycle representation
  9. Thierry Coulhon, Laurent Saloff-Coste, Puissances d'un opérateur régularisant
  10. Daniel W. Stroock, Weian Zheng, Markov chain approximations to symmetric diffusions

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