Skip to main content
SpringerLink
Log in

On the structure of stable random walks

  • Published:
Proceedings of the Indian Academy of Sciences - Mathematical Sciences Aims and scope Submit manuscript

Abstract

We show that the Cauchy random walk on the line, and the Gaussian random walk on the plane are similar as infinite measure preserving transformations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • [A1] Aaronson J, Rational ergodicity and a metric invariant for Markov.Israel J. Math. 27 (1977) 93–123

    Article  MATH  MathSciNet  Google Scholar 

  • [A2] Aaronson J, The intrinsic normalising constants of transformations preserving infinite measures,J. d.’Analyse Math. 49 (1987) 239–270

    Article  MATH  MathSciNet  Google Scholar 

  • [AK] Aaronson J and Keane M, Isomorphism of random walks,Israel J. Math. 87 (1994) 37–64

    Article  MATH  MathSciNet  Google Scholar 

  • [ALP] Aaronson J, Liggett T and Picco P, Equivalence of renewal sequences and isomorphism of and random walks,Israel J. Math. 87 (1994) 65–75

    Article  MATH  MathSciNet  Google Scholar 

  • [AN] Athreya K B and Ney P, A new approach to the limit theory of recurrent Markov chains,T AMS 248 (1978) 493–501

    Article  MathSciNet  Google Scholar 

  • [Ch] Chung K L, Markov Chains with stationary transition probabilities, Vol 104, Springer, Heidelberg, 1960

    MATH  Google Scholar 

  • [Fe] Feller W, An introduction to probability theory and its applications, volume I, (New York: John Wiley) (1968)

    Google Scholar 

  • [Kal] Kaluza T, Uber die Koeffizienten reziproker Potenzreihen,Math. Z. 28 (1928), 161–170.

    Article  MathSciNet  MATH  Google Scholar 

  • [Kin] Kingman J F C, Regenerative Phenomena, (New York: John Wiley) (1972)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematical Sciences, Tel Aviv University, 69978, Tel Aviv, Israel

    Jon Aaronson

Authors
  1. Jon Aaronson
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Aaronson, J. On the structure of stable random walks. Proc. Indian Acad. Sci. (Math. Sci.) 104, 413–419 (1994). https://doi.org/10.1007/BF02863421

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02863421

Keywords

Search

Navigation