Laws of the iterated logarithm for the local times of recurrent random walks on Z2 and of Lévy processes and Random walks in the domain of attraction of Cauchy random variables

Michael B. Marcus; Jay Rosen

Annales de l'I.H.P. Probabilités et statistiques (1994)

  • Volume: 30, Issue: 3, page 467-499
  • ISSN: 0246-0203

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Marcus, Michael B., and Rosen, Jay. "Laws of the iterated logarithm for the local times of recurrent random walks on Z2 and of Lévy processes and Random walks in the domain of attraction of Cauchy random variables." Annales de l'I.H.P. Probabilités et statistiques 30.3 (1994): 467-499. <http://eudml.org/doc/77491>.

@article{Marcus1994,
author = {Marcus, Michael B., Rosen, Jay},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {laws of the iterated logarithm; local times of symmetric Lévy processes; domain of attraction of a stable law; Green function; slowly varying at infinity},
language = {eng},
number = {3},
pages = {467-499},
publisher = {Gauthier-Villars},
title = {Laws of the iterated logarithm for the local times of recurrent random walks on Z2 and of Lévy processes and Random walks in the domain of attraction of Cauchy random variables},
url = {http://eudml.org/doc/77491},
volume = {30},
year = {1994},
}

TY - JOUR
AU - Marcus, Michael B.
AU - Rosen, Jay
TI - Laws of the iterated logarithm for the local times of recurrent random walks on Z2 and of Lévy processes and Random walks in the domain of attraction of Cauchy random variables
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1994
PB - Gauthier-Villars
VL - 30
IS - 3
SP - 467
EP - 499
LA - eng
KW - laws of the iterated logarithm; local times of symmetric Lévy processes; domain of attraction of a stable law; Green function; slowly varying at infinity
UR - http://eudml.org/doc/77491
ER -

References

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  1. [BGT] N. Bingham, C. Goldie and J. Teugels, Regular Variation, 1987, Cambridge Univ. Zbl0617.26001MR898871
  2. [ET] P. Erdös and S.J. Taylor, Some problems concerning the structure of random walk paths, Acta Math. Acad. Sci. Hung., 11, 1960, p. 137-162. Zbl0091.13303MR121870
  3. [F] B. Fristedt, Sample functions of stochastic processes with stationary independent increments, Advances in Probability and Related Topics, 3, 1974, p. 241-396, Marcel Dekker, NY. Zbl0309.60047MR400406
  4. [FP] B. Fristedt and W. Pruitt, Lower functions for increasing random walks and subordinators, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 18, 1971, p. 167-182. Zbl0197.44204MR292163
  5. [K] H. Kesten, Hitting probabilities of single points for processes with stationary independent increments, Memoir N° 93, 1969, Amer. Math. Soc. Zbl0186.50202MR272059
  6. [Ka] J.P. Kahane, Some random series of functions, Heath Math. Monographs, 1968, Cambridge Univ. Press, 1985, 2nd edn. Zbl0192.53801MR833073
  7. [MR1] M.B. Marcus and J. Rosen, Laws of the iterated logarithm for the local times of symmetric Lévy processes and recurrent random walks, 1992, Annals of Probability, To appear. Zbl0815.60073MR1288125
  8. [MR2] M.B. Marcus and J. Rosen, Moment generating functions for the local times of symmetric Markov processes and random walks, Probability in Banach Spaces, 8, 30, 1992, p. 364-378, Birkhauser, Boston. Zbl0788.60092MR1227631
  9. [P] E.J.G. Pitman, Some theorems on characteristic functions of probability distributions, Proc. Fourth Berkeley Symposium, II, 1961, p. 393-402, Univ. of California Press, Berkeley. Zbl0101.35201MR132568

Citations in EuDML Documents

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  1. Michael B. Marcus, Jay Rosen, Laws of the iterated logarithm for intersections of random walks on Z4
  2. N. Gantert, O. Zeitouni, Large and moderate deviations for the local time of a recurrent Markov chain on
  3. Jean Bertoin, Maria-Emilia Caballero, On the rate of growth of subordinators with slowly varying Laplace exponent
  4. Endre Csáki, Pál Révész, Jay Rosen, Functional laws of the iterated logarithm for local times of recurrent random walks on

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