|
The Dynkin-Lamperti arc-sine laws for measure preserving transformations
Author(s):
Maximilian
Thaler
Journal:
Trans. Amer. Math. Soc.
350
(1998),
4593-4607.
MSC (1991):
Primary 28D05, 60F05, 60K05
Retrieve article in:
PDF DVI PostScript
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
Arc-sine laws in the sense of renewal theory are proved for return time processes generated by transformations with infinite invariant measure on sets satisfying a type of Darling-Kac condition, and an application to real transformations with indifferent fixed points is discussed.
References:
- 1.
- J. Aaronson, The asymptotic distributional behaviour of transformations preserving infinite measures, J. Analyse Math. 39 (1981), 203-234 MR 82m:28030
- 2.
- J. Aaronson, Random f-expansions, Ann. Probab. 14 (1986), 1037-1057 MR 87k:60057
- 3.
- J. Aaronson, An introduction to infinite ergodic theory, AMS, 1997 CMP 97:13
- 4.
- N.H. Bingham, C.M. Goldie, J.L. Teugels, Regular variation, Cambridge University Press, Cambridge 1987 MR 88i:26004
- 5.
- D.A. Darling and M. Kac, On occupation times for Markoff processes, Trans. Amer. Math. Soc. 84 (1957), 444-458 MR 18:832a
- 6.
- E.B. Dynkin, Some limit theorems for sums of independent random variables with infinite mathematical expectations, Selected Transl. in Math. Statist. and Probability 1 (1961), 171-189 MR 22:7164
- 7.
- W. Feller, An introduction to probability theory and its applications, Vol. II. John Wiley & Sons, New York 1971 MR 42:5292
- 8.
- J. Lamperti, An occupation time theorem for a class of stochastic processes, Trans. Amer. Math. Soc. 88 (1958), 380-387 MR 20:1372
- 9.
- J. Lamperti, Some limit theorems for stochastic processes, J. Math. Mech. 7 (1958), 433-448 MR 20:4888
- 10.
- P. Manneville, Intermittency, self-similarity and
 spectrum in dissipative dynamical systems, J. Physique 41 (1980), 1235-1243 MR 82e:58065 - 11.
- F. Schweiger, Ergodic theory of fibered systems and metric number theory, Clarendon Press, Oxford 1995 MR 97h:11083
- 12.
- R.S. Slack, Further notes on branching processes with mean one, Z. Wahrscheinlichkeitstheorie verw. Geb. 25 (1972), 31-38 MR 48:9871
- 13.
- M. Thaler, Estimates of the invariant densities of endomorphisms with indifferent fixed points, Isr. J. Math. 37 (1980), 303-314 MR 82f:28021
- 14.
- M. Thaler, Transformations on
![$[0,1]$](/tran/1998-350-11/S0002-9947-98-02312-5/gif-references/img503.gif) with infinite invariant measures, Isr. J. Math. 46 (1983), 67-96 MR 85g:28020 - 15.
- M. Thaler and C. Reichsöllner, Arc sine type limit laws for interval mappings, Manuscript, Salzburg 1986
- 16.
- M. Thaler, A limit theorem for the Perron-Frobenius operator of transformations on
![$[0,1]$](/tran/1998-350-11/S0002-9947-98-02312-5/gif-references/img504.gif) with indifferent fixed points, Isr. J. Math. 91 (1995), 111-127 MR 96i:28020 - 17.
- M. Thaler, The invariant densities for maps modeling intermittency, J. Statist. Phys. 79 (1995), 739-741 MR 96a:58119
- 18.
- R. Zweimüller, Probabilistic properties of dynamical systems with infinite invariant measure, Diplomarbeit, Salzburg 1995
Similar Articles:
Retrieve articles in Transactions of the American Mathematical Society
with MSC
(1991):
28D05, 60F05, 60K05
Retrieve articles in all Journals with MSC
(1991):
28D05, 60F05, 60K05
Additional Information:
Maximilian
Thaler
Affiliation:
Institute of Mathematics University of Salzburg Hellbrunnerstrasse 34 A-5020 Salzburg, Austria
Email:
Maximilian.Thaler@sbg.ac.at
DOI:
10.1090/S0002-9947-98-02312-5
PII:
S 0002-9947(98)02312-5
Received by editor(s):
October 29, 1996
Copyright of article:
Copyright
1998,
American Mathematical Society
|
Comments: webmaster@ams.org