Functional laws of the iterated logarithm for local times of recurrent random walks on Z 2

Endre Csáki; Pál Révész; Jay Rosen

Annales de l'I.H.P. Probabilités et statistiques (1998)

  • Volume: 34, Issue: 4, page 545-563
  • ISSN: 0246-0203

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Csáki, Endre, Révész, Pál, and Rosen, Jay. "Functional laws of the iterated logarithm for local times of recurrent random walks on $Z^2$." Annales de l'I.H.P. Probabilités et statistiques 34.4 (1998): 545-563. <http://eudml.org/doc/77612>.

@article{Csáki1998,
author = {Csáki, Endre, Révész, Pál, Rosen, Jay},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {LIL behaviour; symmetric random walk; scaling limits},
language = {eng},
number = {4},
pages = {545-563},
publisher = {Gauthier-Villars},
title = {Functional laws of the iterated logarithm for local times of recurrent random walks on $Z^2$},
url = {http://eudml.org/doc/77612},
volume = {34},
year = {1998},
}

TY - JOUR
AU - Csáki, Endre
AU - Révész, Pál
AU - Rosen, Jay
TI - Functional laws of the iterated logarithm for local times of recurrent random walks on $Z^2$
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1998
PB - Gauthier-Villars
VL - 34
IS - 4
SP - 545
EP - 563
LA - eng
KW - LIL behaviour; symmetric random walk; scaling limits
UR - http://eudml.org/doc/77612
ER -

References

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  1. [1] J. Bertoin and M. Caballero, On the rate of growth of subordinators with slowly varying Laplace exponent, Sem. de Prob. XXIX, Lecture Notes Math, Vol. 1612, Springer-Verlag, Berlin, 1995, pp. 125-132. Zbl0835.60068MR1459454
  2. [2] L. Breiman, Probability, Society for Industrial andApplied Mathematics, Philadelphia, 1992. Zbl0753.60001MR1163370
  3. [3] E. Csáki, M. Csörgö, A. Földes and P. Révész, On the occupation time of an iterated process having no local time, StochasticProcess. Appl., Vol. 70, 1997, pp. 199-217. Zbl0911.60068MR1475663
  4. [4] P. Erdös and J. Taylor, Some problems concerning the structure of random walk paths, Acta Math. Acad. Sci. Hung., Vol. 11, 1960, pp. 137-162. Zbl0091.13303MR121870
  5. [5] J.-P. Kahane, Some random series of functions, Cambridge University Press, Cambridge, 1985. Zbl0571.60002MR833073
  6. [6] M. Klass, Toward a universal law of the iterated logarithm, Part I, Z. Wahrsch. verw. Gebiete, Vol. 36, 1976, pp. 165-178. Zbl0319.60019MR415742
  7. [7] M. Marcus and J. Rosen, Laws of the iterated logarithm for the local times of recurrent random walks on Z2 and of Levy processes and recurrent random walks in the domain of attraction of Cauchy random variables, Ann. Inst. H. Poincaré Prob. Stat., Vol. 30, 1994, pp. 467-499. Zbl0805.60069MR1288360
  8. [8] M. Marcus and J. Rosen, Laws of the iterated logarithm for the local times of symmetric Levy processes and recurrent random walks, Ann. Probab., Vol. 22, 1994, pp. 626-658. Zbl0815.60073MR1288125
  9. [9] P. Révész and E. Willekens, On the maximal distance between two renewal epochs, StochasticProcess. Appl., Vol. 27, 1988, pp. 21-41. Zbl0632.60083MR934527

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