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18,215
CENTRAL LIMIT THEOREM FOR DETERMINISTIC SYSTEMS
, 1996
"... A unified approach to obtaining the central limit theorem for hyperbolic dynamical systems is presented. It builds on previous results for one dimensional maps but it applies to the multidimensional case as well. ..."
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Cited by 77 (4 self)
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A unified approach to obtaining the central limit theorem for hyperbolic dynamical systems is presented. It builds on previous results for one dimensional maps but it applies to the multidimensional case as well.
CENTRAL LIMIT THEOREM ON HYPERGROUPS
"... Abstract. On the basis of Heyer and Zeuner’s results we will treat the central limit theorem for probability measures on hypergroup. The purpose of this article is to verify a central limit theorem for random variables which take their values in a hypergroup. However the special case that G is the o ..."
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Abstract. On the basis of Heyer and Zeuner’s results we will treat the central limit theorem for probability measures on hypergroup. The purpose of this article is to verify a central limit theorem for random variables which take their values in a hypergroup. However the special case that G
Central Limits and Financial Risk
, 2009
"... Systematic model bias has been implicated in the global recession that began in 2007, and this bias can be traced back to assumptions about the normality of data. Nonetheless, the normal distribution continues to play a foundational role in quantitative finance. One reason for this is that the norma ..."
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for this is that the normal often emerges, without prompting, as the distribution of sums or averages of large collections of random variables. Precise statements of this miracle are known as Central Limit Theorems, and they appear throughout the physical and social sciences. In this note, we review some of the most widely
MONOTONIC APPROACH TO CENTRAL LIMITS
, 2000
"... (Communicated by WeiYin Loh) Abstract. The approach to limits guaranteed by the Central Limit Theorem appears to be monotonic in many cases. A variety of empirical examples are discussed. Proofs are given for some special cases of the binomial, gamma, and Poisson distributions. 1. Monotonicity phen ..."
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Cited by 1 (0 self)
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(Communicated by WeiYin Loh) Abstract. The approach to limits guaranteed by the Central Limit Theorem appears to be monotonic in many cases. A variety of empirical examples are discussed. Proofs are given for some special cases of the binomial, gamma, and Poisson distributions. 1. Monotonicity
Central Limit Theorems and Proofs
"... The following gives a selfcontained treatment of the central limit theorem (CLT). It is based on Lindeberg’s (1922) method. To state the CLT which we shall prove, we introduce the following notation. We assume that Xn1,..., Xnn are independent random variables with means 0 and respective variances ..."
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The following gives a selfcontained treatment of the central limit theorem (CLT). It is based on Lindeberg’s (1922) method. To state the CLT which we shall prove, we introduce the following notation. We assume that Xn1,..., Xnn are independent random variables with means 0 and respective variances
Bootstrap with . . . Central Limit Theorems.
, 1990
"... We consider "bootstrap" estimators of the distribution of the empirical process, indexed by a class offunctions F, that emerge by weighting the data by multipliers ~ / 2:]=1 Yj, for iid positive random variables, Yll Y2, ••• • Assuming that the ~'s satisfy the L2,1 integrability condi ..."
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condition fo oo Jp(IY11> t) dt < 00, we prove that FE CLT(P) and PF2: = P(suPfEFlf(x)1)2 < 00, is necessary and sufficient for the bootstrap central limit theorem to hold, almost surely, and F E CLT(P) for it to hold "in probability". These results parallel those of Cine and Zinn (1990
CENTRAL LIMIT THEOREMS FOR RECORDS
"... Abstract. Consider a sequence (Xn) of independent and identically distributed random variables, taking nonnegative integer values and call Xn a record if Xn> max{X1,..., Xn−1}. In Gouet et al. (2001), a martingale approach combined with asymptotic results for sums of partial minima was used to de ..."
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to derive strong convergence results for the number of records among the first n observations. Now, in this paper we exploit the connection between records and martingales to establish a central limit theorem for the number of records in many discrete distributions, identifying the centering and scaling
The Bosonic Central Limit Theorem
, 2002
"... The aim of this article is to give an overview on recent progress of the central limit theorem for mixing quantum spin chains. The limit theorem we discuss here is described in the language of operator algebras. $(\mathrm{c}.\mathrm{f} $. [4], [5] $) $ We consider the following one dimensional quant ..."
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The aim of this article is to give an overview on recent progress of the central limit theorem for mixing quantum spin chains. The limit theorem we discuss here is described in the language of operator algebras. $(\mathrm{c}.\mathrm{f} $. [4], [5] $) $ We consider the following one dimensional
GENERATING FUNCTIONS AND CENTRAL LIMIT THEOREMS
"... • Sums of independent random variables and powers of generating functions • A central limit theorem • Bivariate generating functions ..."
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• Sums of independent random variables and powers of generating functions • A central limit theorem • Bivariate generating functions
On Convergence Rates in the Central Limit Theorems for Combinatorial Structures
, 1998
"... Flajolet and Soria established several central limit theorems for the parameter "number of components" in a wide class of combinatorial structures. In this paper, we shall prove a simple theorem which applies to characterize the convergence rates in their central limit theorems. This th ..."
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Cited by 77 (10 self)
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Flajolet and Soria established several central limit theorems for the parameter "number of components" in a wide class of combinatorial structures. In this paper, we shall prove a simple theorem which applies to characterize the convergence rates in their central limit theorems
Results 1  10
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18,215