Recurrent random walks on certain classes of groups

  • Paolo Baldi
Article
Received:

Abstract

This article is divided into two parts: in the first we give some results about renewal and normality of a recurrent random walk (r.w.) on an abelian group, without the Harris hypothesis, which will extend the theorems of S.C. Port and C.J. Stone ([8]) to a larger class of functions. They are stated in the Theorems 1.14 and 1.15. The technique will be to approximate the recurrent r.w. by a Harris recurrent r.w., for which the recent results of A. Brunel and D. Revuz ([2–4]) hold.

the second part the results of the first part are extended to a particular class of nonabelian groups.

The author wishes to thank A. Brunel for several very useful conversations and suggestions.

Keywords

Stochastic Process Random Walk Probability Theory Abelian Group Recent Result 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. 1.
    Baldi, P.: Sur l'équation de Poisson. Ann. Inst. H. Poincaré 10, 423–434 (1974)Google Scholar
  2. 2.
    Brunel, A., Revuz, D.: Marches de Harris sur les groupes localement compacts I. Ann. école Normale Sup. 4ème série, 7, 273–310 (1974)Google Scholar
  3. 3.
    Brunel, A., Revuz, D.: Marches de Harris sur les groupes localement compacts II (To appear in the Bull. Soc. Math. France)Google Scholar
  4. 4.
    Brunel, A., Revuz, D.: Marches de Harris sur les groupes localement compacts IV. (To appear)Google Scholar
  5. 5.
    Gorostiza, L. G.: Limit random motions of Euclidean space. Ann. Probability 1 (4), 603–612 (1973)Google Scholar
  6. 6.
    Mukherjea, A.: Limit theorems for probability measures on non-compact groups and semi-groups. (To appear)Google Scholar
  7. 7.
    Neveu, J.: Potentiel markovien récurrent des chaÎnes de Harris. Ann. Inst. Fourier 22, 85–130 (1972)Google Scholar
  8. 8.
    Port, S. C., Stone, G. J.: Potential theory of random walks on abelian groups. Acta Math. 122, 19–114 (1969)Google Scholar
  9. 9.
    Rudin, W.: Fourier Analysis on groups. New York: J. Wiley 1962Google Scholar

Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • Paolo Baldi
    • 1
  1. 1.Université Pierre et Marie CurieLaboratoire de Calcul des ProbabilitésParis Cedex 05France

Personalised recommendations