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Functional Central Limit Theorems
2008Central limit theorems guarantee that the distributions of properly normalized sums of certain random variables are approximately normal. In many cases, however, a more detailed analysis is necessary. When testing for structural constancy in models, we might be interested in the temporal evolution of our sums.
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On the universal A.S. central limit theorem
Acta Mathematica Hungarica, 2007Let \(X_1 ,X_2 ,\dots\) be independent random variables such that for some measurable functions \(g_l \) the weak limit theorem \(g_l (X_1 ,\dots,X_l ) \Rightarrow G\) holds with some distribution function \(G\). The paper gives conditions for the validity of relation \(D_N^{ - 1} \sum\limits_{k = 1}^N {d_k f(g_k (X_1 ,\dots,X_k ))} =\int_{ - \infty }^\
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Scandinavian Actuarial Journal, 1944
If X and Y are mutually independent random variables whith the d. f. 1 F 1(χ) and F 2(χ), it is known 2 that the sum X + Y has the d. f. F 2(χ), defined as the convolution where the integrals are Lebesgue-Stiltjes integrals. One uses the abbreviation More generally the sum X 1 + X 2 + … + X n of n mutually independent random variables with the d. f.
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If X and Y are mutually independent random variables whith the d. f. 1 F 1(χ) and F 2(χ), it is known 2 that the sum X + Y has the d. f. F 2(χ), defined as the convolution where the integrals are Lebesgue-Stiltjes integrals. One uses the abbreviation More generally the sum X 1 + X 2 + … + X n of n mutually independent random variables with the d. f.
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2003
The Central Limit Theorem is one of the classical results in statistics with many applications in actuarial mathematics, finance, and risk management and a host of other not necessarily economic disciplines. In Chapter 14 we will apply it to the derivation of the Black—Scholes formula from the binomial Cox—Ross—Rubinstein model.
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The Central Limit Theorem is one of the classical results in statistics with many applications in actuarial mathematics, finance, and risk management and a host of other not necessarily economic disciplines. In Chapter 14 we will apply it to the derivation of the Black—Scholes formula from the binomial Cox—Ross—Rubinstein model.
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2012
The law of large numbers states that the arithmetic mean of independent, identically distributed random variables converges to the expected value. One interpretation of the central limit theorem is as a (distributional) rate result.
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The law of large numbers states that the arithmetic mean of independent, identically distributed random variables converges to the expected value. One interpretation of the central limit theorem is as a (distributional) rate result.
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On the Multidimensional Central Limit Theorem
Theory of Probability & Its Applications, 1968openaire +1 more source
Central limit theorem and almost sure central limit theorem for the product of some partial sums
Proceedings of the Indian Academy of Sciences: Mathematical Sciences, 2008Yu Miao
exaly
A general central limit theorem under sublinear expectations
Science China Mathematics, 2010Yufeng Shi, Shi Yufeng
exaly