Approximation by Brownian motion for Gibbs measures and flows under a function

Ergodic Theory and Dynamical Systems

Volumn 4, Issue 4, 1984, Pages 541-552

  Philipp, Walter ^b  

^a UNIVERSITY OF GÖTTINGEN   (Germany)

^b UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000454046     PISSN: 01433857     EISSN: 14694417     Source Type: Journal    
DOI: 10.1017/S0143385700002637     Document Type: Article

References (10)

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3. Doob J. L. Stochastic Processes. J. Wiley: New York, 1953.
4. Ibragimov I. A. Some limit theorems for stationary processes. Theor. Probability Appl. 7 (1962) 349–382.10.1137/1107036
5. Philipp W. & Stout W. Almost sure invariance principles for partial sums of weakly dependent random variables. Mem. Amer. Math. Soc. 161 (1975).
6. Ratner M. The central limit theorem for geodesic flows on n-dimensional manifolds of negative curvature. Israel J. Math. 16 (1973), 181–197.10.1007/BF02757869
7. Renyi A. Wahrscheinlichkeitsrechnung. Deutscher Verlag Wissensch.: Berlin, 1962.
8. Ruelle D., Statistical mechanics of a one-dimensional lattice gas. Commun. Math. Phys. 9 (1968), 267–278.10.1007/BF016542810234697
9. Serfling R. J., Moment inequalities for the maximum cumulative sum. Ann. Math. Stat. 41 (1970), 1227–1234 10.1214/aoms/11776968980268938
10. Sinai Y. G., Gibbs measures in ergodic theory. Uspeki Mat. Nauk (4) 27 (1972), 21–63.