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Assume that a renormalized Birkhoff sum $S_n f/B_n$ converges in distribution to a nontrivial limit. What can one say about the sequence $B_n$? Most natural statements in the literature involve sequences $B_n$ of the form $B_n = n^\alpha L(n)$, where $L$ is slowly varying. We will discuss the possible growth rate of $B_n$ both in the probability preserving case and the conservative case. In particular, we will describe examples where $B_n$ grows superpolynomially, or where $B_{n+1}/B_n$ does not tend to $1$. Assume that a renormalized Birkhoff sum $S_n f/B_n$ converges in distribution to a nontrivial limit. What can one say about the sequence $B_n$? Most natural statements in the literature involve sequences $B_n$ of the form $B_n = n^\alpha L(n)$, where $L$ is slowly varying. We will discuss the possible growth rate of $B_n$ both in the probability preserving case and the conservative case. In particular, we will describe examples where $B_n$ ...

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Documents 60F05 | enregistrements trouvés : 139

​​​Growth of normalizing sequences in limit theorems Gouëzel, Sébastien | CIRM H Nouveau

On the weak invariance principle and its quenched version under projective criteria Merlevède, Florence | CIRM Nouveau

Autour de la géométrie stochastique : polytopes aléatoires et autres modèles Calka, Pierre | CIRM H Nouveau

Problems in the constructive trend in mathematics V Orevkov, V. P. ; Sanin, N. A. | American Mathematical Society 1972 Nouveau

Problems in the constructive trend in mathematics IV Orevkov, V. P. ; Sanin, M. A. | American Mathematical Society 1970 Nouveau

Problems in the constructive trend in mathematics VI Orevkov, V. P. ; Sanin, N. A. | American Mathematical Society 1976 Nouveau

Ecole d'été de probabilités de Saint-Flour XIII - 1983 :13ème école d'été de probabilités de Saint-Flour#Juil. 3-20 Aldous, D. J. ; Ibragimov, I. A. ; Jacod, J. ; Hennequin, P. L. | Springer-Verlag 1985 Nouveau

Geometrical and statistical aspects of probability in banach spaces :actes des journées S.M.F. de calcul des probabilités dans les espaces de Banach#Juin19-20 Fernique, X. ; Heinkel, B. ; Marcus, M. B. ; Meyer, P. A. | Springer-Verlag 1986 Nouveau

Stability problems for stochastic models :proceedings of the 9th international seminar held in varna#May 13-19 Kalashnikov, V. V. ; Penkov, B. ; Zolotarev, V. M. | Springer-Verlag 1987 Nouveau

Uniform limit theorems for sums of independent random variables Arak, T. V. ; Zaitsev, A. Yu. ; Ibragimov, I. A. | American Mathematical Society 1988 Nouveau

Limit theorems in probability and statisticsthird hungarian colloquium on...organized in pecs,hungary,july 3-7,1989 Berkes, I. ; Csaki, E. ; Revesz, P. | North-Holland Publishing Co. 1990 Nouveau

Stability problems for stochastic modelsproceedings of the 11th international seminar held in Sukhumi (Abkhazian autonomous republic) USSR, Sept. 25- Oct. 1, 1987 Kalashnikov, V. V. ; Zolotarev, V. M. | Springer-Verlag 1989 Nouveau

Probability and information theoryproceedings of the international symposium at McMaster universityApril 4-5 Behara, Minaketan ; Krickeberg , K. ; Wolfowitz, J. | Springer-Verlag 1969 Nouveau

Probabilistic methods in differential equationsproceedings of the conference held at the University of Victoria, British ColumbiaAug. 19-20 Pinsky, M. A. | Springer-Verlag 1975 Nouveau

Proceedings of the sixth Berkeley symposium on mathematical statistics and probability. Vol. 2probability theoryheld at the Statistical Laboratory, University of CaliforniaJune 21 - July 18 Le Cam, Lucien ; Neyman, Jerzy ; Scott, Elizabeth | University Of California Press 1972 Nouveau

Probabilities and metricsconvergence of laws on metric spaces, with a view to statistical testing Dudley, R. M. | Aarhus Universitet Matematisk Institut 1976 Nouveau

Necessary and sufficient conditions for the uniform convergence of Random trigonometric series Marcus, M. B. ; Pisier, G. | Aarhus Universitet Matematisk Institut 1978 Nouveau

The calculus of non-measurable functions and sets Andersen, N. T. | Mathematics Institute University 1985 Nouveau

Qualitative effects in the estimates of the convergencee rate in the central limit theorem in multidimensional spaces Senatov, V. V. | Steklov Institute of Mathematics 1996 Nouveau

Algebraic methods in statistics and probability :AMS special session on ... held at University of Notre Dame#April 8-9 Viana, Marlos A. G. ; Richards, Donald St. P. | Amercian Mathematical Society 2001 Nouveau

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Growth of normalizing sequences in limit theorems Gouëzel, Sébastien | CIRM H Nouveau

Ecole d'été de probabilités de Saint-Flour XIII - 1983 :
13ème école d'été de probabilités de Saint-Flour#Juil. 3-20 Aldous, D. J. ; Ibragimov, I. A. ; Jacod, J. ; Hennequin, P. L. | Springer-Verlag 1985 Nouveau

Geometrical and statistical aspects of probability in banach spaces :
actes des journées S.M.F. de calcul des probabilités dans les espaces de Banach#Juin19-20 Fernique, X. ; Heinkel, B. ; Marcus, M. B. ; Meyer, P. A. | Springer-Verlag 1986 Nouveau

Stability problems for stochastic models :
proceedings of the 9th international seminar held in varna#May 13-19 Kalashnikov, V. V. ; Penkov, B. ; Zolotarev, V. M. | Springer-Verlag 1987 Nouveau

Limit theorems in probability and statistics
third hungarian colloquium on...organized in pecs,hungary,july 3-7,1989 Berkes, I. ; Csaki, E. ; Revesz, P. | North-Holland Publishing Co. 1990 Nouveau

Stability problems for stochastic models
proceedings of the 11th international seminar held in Sukhumi (Abkhazian autonomous republic) USSR, Sept. 25- Oct. 1, 1987 Kalashnikov, V. V. ; Zolotarev, V. M. | Springer-Verlag 1989 Nouveau

Probability and information theory
proceedings of the international symposium at McMaster university
April 4-5 Behara, Minaketan ; Krickeberg , K. ; Wolfowitz, J. | Springer-Verlag 1969 Nouveau

Probabilistic methods in differential equations
proceedings of the conference held at the University of Victoria, British Columbia
Aug. 19-20 Pinsky, M. A. | Springer-Verlag 1975 Nouveau

Proceedings of the sixth Berkeley symposium on mathematical statistics and probability. Vol. 2
probability theory
held at the Statistical Laboratory, University of California
June 21 - July 18 Le Cam, Lucien ; Neyman, Jerzy ; Scott, Elizabeth | University Of California Press 1972 Nouveau

Probabilities and metrics
convergence of laws on metric spaces, with a view to statistical testing Dudley, R. M. | Aarhus Universitet Matematisk Institut 1976 Nouveau

Algebraic methods in statistics and probability :
AMS special session on ... held at University of Notre Dame#April 8-9 Viana, Marlos A. G. ; Richards, Donald St. P. | Amercian Mathematical Society 2001 Nouveau