Authors:
Endre Csáki Alfréd Rényi Institute of Mathematics, Budapest, P.O.B. 127, H-1364, Hungary

Search for other papers by Endre Csáki in
Current site
Google Scholar
PubMed
Close
and
Antónia Földes Department of Mathematics, College of Staten Island, CUNY, 2800 Victory Blvd., Staten Island, New York 10314, U.S.A

Search for other papers by Antónia Földes in
Current site
Google Scholar
PubMed
Close
Open access

We study the path behavior of the symmetric walk on some special comb-type subsets of ℤ2 which are obtained from ℤ2 by generalizing the comb having finitely many horizontal lines instead of one.

  • [1]

    BERTACCHI, D. Asymptotic behaviour of the simple random walk on the 2-dimensional comb. Electron. J. Probab. 11 (2006), 11841203.

  • [2]

    BERTOIN, J. Iterated Brownian motion and stable (1/4) subordinator. Statist. Probab. Lett. 27(1996), 111114.

  • [3]

    CHUNG, K. L. On the maximum partial sums of sequences of independent random variables.Trans. Amer. Math. Soc. 64 (1948), 205233.

  • [4]

    CSÁKI, E., CSÖRGŐ, M., FÖLDES, A. AND RÉVÉSZ, P. How big are the increments of the local time of a Wiener process? Ann. Probab. 11,(1983), 593608.

    • Search Google Scholar
    • Export Citation
  • [5]

    CSÁKI, E., CSÖRGŐ, M., FÖLDES, A. AND RÉVÉSZ, P. Global Strassen-type theorems for iterated Brownian motions. Stochastic Process. Appl. 59 (1995), 321341.

    • Search Google Scholar
    • Export Citation
  • [6]

    CSÁKI, E., CSÖRGŐ, M., FÖLDES, A. AND RÉVÉSZ, P. Strong limit theorems for a simple random walk on the 2-dimensional comb. Electron. J. Probab. 14 (2009), 23712390.

    • Search Google Scholar
    • Export Citation
  • [7]

    CSÁKI, E., CSÖRGŐ, M., FÖLDES, A. AND RÉVÉSZ, P. Strong limit theorems for anisotropic random walks on Z2. Periodica Math. Hungar. 67 (2013), 7194.

    • Search Google Scholar
    • Export Citation
  • [8]

    CSÁKI, E. AND FÖLDES, A. How big are the increments of the local time of a recurrent random walk? Z. Wahrsch. Verw. Gebiete 65 (1983), 307322.

    • Search Google Scholar
    • Export Citation
  • [9]

    CSÁKI, E., FÖLDES, A. AND RÉVÉSZ, P. Some results and problems for anisotropic random walk on the plane. Asymptotic Laws and Methods in Stochastics. A volume in Honour of Miklós Csörgő. Fields Institute Communication 76 2015, pp. 5576.

    • Search Google Scholar
    • Export Citation
  • [10]

    CSÁKI, E. AND FÖLDES, A. Random walks on comb-type subsets of Z2. Journal of Theoretical Probability 33 (2020), 22332257.

  • [11]

    CSÁKI, E. AND FÖLDES, A. Strong Approximation of the Anisotropic Random Walk Revisited. Journal of Theoretical Probability 35 (2022), 18792895.

    • Search Google Scholar
    • Export Citation
  • [12]

    CSÁKI, E. AND RÉVÉSZ, P. Strong invariance for local time. Z. Wahrsch. verw. Gebiete 50 (1983), 525.

  • [13]

    CSÖRGŐ, M. AND RÉVÉSZ, P. How big are the increments of a Wiener process? Ann. Probab. 7 (1979), 731737.

  • [14]

    HEYDE, C. C. On the asymptotic behavior of random walks on an anisotropic lattice. J. Statist. Physics 27 (1982), 721730.

  • [15]

    HEYDE, C. C. Asymptotics for two-dimensional anisotropic random walks. In: Stochastic Processes. Springer, New York, 1993, pp. 125130.

    • Search Google Scholar
    • Export Citation
  • [16]

    HIRSCH, W. M. A strong law for the maximum cumulative sum of independent random variables. Comm. Pure Appl. Math. 18 (1965), 109127.

  • [17]

    KESTEN, H. An iterated logarithm law for the local time. Duke Math. J. 32 (1965), 447456.

  • [18]

    NANE, E. Laws of the iterated logarithm for a class of iterated processes. Statist. Probab. Lett. 79 (2009), 17441751.

  • [19]

    RÉVÉSZ, P. Local time and invariance. Lecture Notes in Math. 861, 1981, pp. 128145. Springer, New York.

  • [20]

    RÉVÉSZ, P. Random Walk in Random and Non-Random Environments, 3rd ed. World Scientific, Singapore, 2013.

  • [21]

    TÓTH, B. No more than three favorite sites for simple random walk. Ann. Probab. 29 (2001), 484503.

  • [22]

    WILLIAMS, D. Probability with Martingales. Cambridge University Press, Great Britain, 1991.

  • Collapse
  • Expand
The Instruction for Authors is available in PDF format. Please, download the file from HERE.
Please, download the LaTeX template from HERE.

Editor in Chief: László TÓTH (University of Pécs)

Honorary Editors in Chief:

  • † István GYŐRI (University of Pannonia, Veszprém, Hungary)
  • János PINTZ (Rényi Institute of Mathematics, Budapest, Hungary)
  • Ferenc SCHIPP (Eötvös Loránd University, Budapest, Hungary and University of Pécs, Pécs, Hungary)
  • Sándor SZABÓ (University of Pécs, Pécs, Hungary)
     

Deputy Editors in Chief:

  • Erhard AICHINGER (JKU Linz, Linz, Austria)
  • Ferenc HARTUNG (University of Pannonia, Veszprém, Hungary)
  • Ferenc WEISZ (Eötvös Loránd University, Budapest, Hungary)

Editorial Board

  • Attila BÉRCZES (University of Debrecen, Debrecen, Hungary)
  • István BERKES (Rényi Institute of Mathematics, Budapest, Hungary)
  • Károly BEZDEK (University of Calgary, Calgary, Canada)
  • György DÓSA (University of Pannonia, Veszprém, Hungary)
  • Balázs KIRÁLY – Managing Editor (University of Pécs, Pécs, Hungary)
  • Vedran KRCADINAC (University of Zagreb, Zagreb, Croatia) 
  • Željka MILIN ŠIPUŠ (University of Zagreb, Zagreb, Croatia)
  • Gábor NYUL (University of Debrecen, Debrecen, Hungary)
  • Margit PAP (University of Pécs, Pécs, Hungary)
  • István PINK (University of Debrecen, Debrecen, Hungary)
  • Mihály PITUK (University of Pannonia, Veszprém, Hungary)
  • Lukas SPIEGELHOFER (Montanuniversität Leoben, Leoben, Austria)
  • Andrea ŠVOB (University of Rijeka, Rijeka, Croatia)
  • Csaba SZÁNTÓ (Babeş-Bolyai University, Cluj-Napoca, Romania)
  • Jörg THUSWALDNER (Montanuniversität Leoben, Leoben, Austria)
  • Zsolt TUZA (University of Pannonia, Veszprém, Hungary)

Advisory Board

  • Szilárd RÉVÉSZ (Rényi Institute of Mathematics, Budapest, Hungary)  - Chair
  • Gabriella BÖHM
  • György GÁT (University of Debrecen, Debrecen, Hungary)

University of Pécs,
Faculty of Sciences,
Institute of Mathematics and Informatics
Department of Mathematics
7624 Pécs, Ifjúság útja 6., HUNGARY
(36) 72-503-600 / 4179
ltoth@gamma.ttk.pte.hu

  • Mathematical Reviews
  • Zentralblatt
  • DOAJ

Publication Model Gold Open Access
Submission Fee none
Article Processing Charge 0 EUR/article (temporarily)
Subscription Information Gold Open Access

Mathematica Pannonica
Language English
Size A4
Year of
Foundation
1990
Volumes
per Year
1
Issues
per Year
2
Founder Akadémiai Kiadó
Founder's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Publisher Akadémiai Kiadó
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 2786-0752 (Online)
ISSN 0865-2090 (Print)