Relevant bibliographies by topics / Central limit theorem

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Central limit theorem'

Author: Grafiati
Published: 4 June 2021
Last updated: 29 July 2024

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Journal articles on the topic "Central limit theorem"

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Bianucci, Marco. "Operators central limit theorem." Chaos, Solitons & Fractals 148 (July 2021): 110961. http://dx.doi.org/10.1016/j.chaos.2021.110961.

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Bulinski, A. V. "Conditional Central Limit Theorem." Theory of Probability & Its Applications 61, no. 4 (January 2017): 613–31. http://dx.doi.org/10.1137/s0040585x97t98837x.

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de Jong, Robert M. "Central Limit Theorems for Dependent Heterogeneous Random Variables." Econometric Theory 13, no. 3 (June 1997): 353–67. http://dx.doi.org/10.1017/s0266466600005843.

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This paper presents central limit theorems for triangular arrays of mixingale and near-epoch-dependent random variables. The central limit theorem for near-epoch-dependent random variables improves results from the literature in various respects. The approach is to define a suitable Bernstein blocking scheme and apply a martingale difference central limit theorem, which in combination with weak dependence conditions renders the result. The most important application of this central limit theorem is the improvement of the conditions that have to be imposed for asymptotic normality of minimization estimators.
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Fazekas, István, and Alexey Chuprunov. "Almost sure limit theorems for random allocations." Studia Scientiarum Mathematicarum Hungarica 42, no. 2 (May 1, 2005): 173–94. http://dx.doi.org/10.1556/sscmath.42.2005.2.4.

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Almost sure limit theorems are presented for random allocations. A general almost sure limit theorem is proved for arrays of random variables. It is applied to obtain almost sure versions of the central limit theorem for the number of empty boxes when the parameters are in the central domain. Almost sure versions of the Poisson limit theorem in the left domain are also proved.
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Roginsky, Allen L. "A Central Limit Theorem for Cumulative Processes." Advances in Applied Probability 26, no. 1 (March 1994): 104–21. http://dx.doi.org/10.2307/1427582.

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A central limit theorem for cumulative processes was first derived by Smith (1955). No remainder term was given. We use a different approach to obtain such a term here. The rate of convergence is the same as that in the central limit theorems for sequences of independent random variables.
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Roginsky, Allen L. "A Central Limit Theorem for Cumulative Processes." Advances in Applied Probability 26, no. 01 (March 1994): 104–21. http://dx.doi.org/10.1017/s0001867800026033.

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A central limit theorem for cumulative processes was first derived by Smith (1955). No remainder term was given. We use a different approach to obtain such a term here. The rate of convergence is the same as that in the central limit theorems for sequences of independent random variables.
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LIEBSCHER, VOLKMAR. "NOTE ON ENTANGLED ERGODIC THEOREMS." Infinite Dimensional Analysis, Quantum Probability and Related Topics 02, no. 02 (June 1999): 301–4. http://dx.doi.org/10.1142/s0219025799000175.

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We prove the entangled ergodic theorem, a notion recently proposed by Accardi, Hashimoto and Obata in connection with central limit theorems1 provided a multidimensional noncommutative analogue of the spectral theorem is valid. This shows at least the possible structure of limit states in such central limit theorems.
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Corcoran, Mimi. "Illustrating the Central Limit Theorem." Mathematics Teacher 109, no. 6 (February 2016): 456–62. http://dx.doi.org/10.5951/mathteacher.109.6.0456.

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Shashkin, A. P. "On Newman's Central Limit Theorem." Theory of Probability & Its Applications 50, no. 2 (January 2006): 330–37. http://dx.doi.org/10.1137/s0040585x97981731.

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Mitic, P. "The central limit theorem visualised." Teaching Mathematics and its Applications 15, no. 2 (June 1, 1996): 84–90. http://dx.doi.org/10.1093/teamat/15.2.84.

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Dissertations / Theses on the topic "Central limit theorem"

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Alcântara, Daniel Tomás Vital de. "Central limit theorem variations." Master's thesis, Instituto Superior de Economia e Gestão, 2019. http://hdl.handle.net/10400.5/20409.

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Mestrado em Mathematical Finance
Um dos teoremas mais importantes da Teoria da Probabilidade é o Teorema do Limite Central. Este afirma que se Xn é uma sequência de variáveis aleatórias então as somas parciais normalizadas convergem para a distribuição normal. Além disso a ausência de pré condições faz-nos perguntar-nos se generalizações são possíveis. Particularmente neste manuscrito vamos focar-nos em duas questões: Existe uma taxa de convergência (universal) para o Teorema do Limite Central? Além disso em que circunstâncias podemos aplicar o Teorema do Limite Central? O teorema de Continuidade de Lévy afirma que a convergência em distribuição é equivalente à convergência nas funções características. Além disso quando aplicamos as expansões de Taylor a funções características ficamos com um polinómios com os momentos da variável como coeficientes. Por estas razões no nosso caso fazer os cálculos com funções características é preferível. Pelo teorema de Berry Essen podemos, de facto, encontrar a taxa de convergência que procuramos. E pelo teorema de Lindeberg e condição de Lyapunov podemos descobrir que o Teorema do Limite Central pode aplicar-se a sequências que não são identicamente distribuídas. Finalmente, utilizando o teorema ergódico vamos explicar como processos estocásticos estão relacionados com a teoria ergódica. Com isto vamos mostrar como este teorema pode ser utilizado pata encontrar um resultado quando a sequencia não é independente.
One of the most important theorems of Probability Theory is the Central Limit Theorem. It states that if Xn is a sequence of random variables then the normal- ized partial sums converge to a normal distribution. This result omits any rate of convergence. Furthermore the lack of assumptions makes us wonder if some gener- alizations are possible. Particularly in this essay we will focus on two questions: Does it exist a (uni- versal) rate of convergence for the Central Limit Theorem? Furthermore in which circumstances can we apply the Central Limit Theorem? The Lévy Continuity Theorem states that convergence on distribution functions is equivalent to convergence on characteristic functions. Furthermore when we ap- ply Taylor expansions to characteristic functions we get a polynomial with the mo- ments as coefficients. For these reasons, on our case computing with characteristic functions is preferable. By the Berry Essen Theorem we can in fact find the rate of convergence we are looking for. And by the Lindeberg Theorem and Lyapunov Condition we find that the Central Limit Theorem applies to sequences that are not identically distributed. Finally, using the Ergodic Theorem we will explain how stochastic processes are related to Ergodic Theory. With this we will show how this theorem can be used to find a result when the sequence is not independent.
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ALVES, RODRIGO BARRETO. "MARTINGALE CENTRAL LIMIT THEOREM." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2017. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=32327@1.

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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO
COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
PROGRAMA DE SUPORTE À PÓS-GRADUAÇÃO DE INSTS. DE ENSINO
PROGRAMA DE EXCELENCIA ACADEMICA
Esta dissertação é dedicada ao estudo das taxas de convergência no Teorema Central do Limite para Martingais. Começamos a primeira parte da tese apresentando a Teoria de Martingais, introduzindo o conceito de esperança condicional e suas propriedades. Desta forma poderemos descrever o que é um Martingal, mostraremos alguns exemplos, e exporemos alguns dos seus principais teoremas. Na segunda parte da tese vamos analisar o Teorema Central do Limite para variáveis aleatórias, apresentando os conceitos de função característica e convergência em distribuição, que serão utilizados nas provas de diferentes versões do Teorema Central do Limite. Demonstraremos três formas do Teorema Central do Limite, para variáveis aleatórias independentes e identicamente distribuídas, a de Lindeberg-Feller e para uma Poisson. Após, apresentaremos o Teorema Central do Limite para Martingais, demonstrando uma forma mais geral e depois enunciaremos uma forma mais específica a qual focaremos o resto da tese. Por fim iremos discutir as taxas de convergência no Teorema Central do Limite, com foco nas taxas de convergência no Teorema Central do Limite para Martingais. Em particular, exporemos o resultado de [4], o qual determina, até uma constante multiplicativa, a dependência ótima da taxa de um certo parâmetro do martingal.
This dissertation is devoted to the study of the rates of convergence in the Martingale Central Limit Theorem. We begin the first part presenting the Martingale Theory, introducing the concept of conditional expectation and its properties. In this way we can describe what a martingale is, present examples of martingales, and state some of the principal theorems and results about them. In the second part we will analyze the Central Limit Theorem for random variables, presenting the concepts of characteristic function and the convergence in distribution, which will be used in the proof of various versions of the Central Limit Theorem. We will demonstrate three different forms of the Central Limit Theorem, for independent and identically distributed random variables, Lindeberg-Feller and for a Poisson distribution. After that we can introduce the Martingale Central Limit Theorem, demonstrating a more general form and then stating a more specific form on which we shall focus. Lastly, we will discuss rates of convergence in the Central Limit Theorems, with a focus on the rates of convergence in the Martingale Central Limit Theorem. In particular, we state results of [4], which determine, up to a multiplicative constant, the optimal dependence of the rate on a certain parameter of the martingale.
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Sorokin, Yegor. "Probability theory, fourier transform and central limit theorem." Manhattan, Kan. : Kansas State University, 2009. http://hdl.handle.net/2097/1604.

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Jiang, Xinxin. "Central limit theorems for exchangeable random variables when limits are mixtures of normals /." Thesis, Connect to Dissertations & Theses @ Tufts University, 2001.

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Thesis (Ph.D.)--Tufts University, 2001.
Adviser: Marjorie G. Hahn. Submitted to the Dept. of Mathematics. Includes bibliographical references (leaves44-46). Access restricted to members of the Tufts University community. Also available via the World Wide Web;
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Pramukkul, Pensri. "Temporal Complexity and Stochastic Central Limit Theorem." Thesis, University of North Texas, 2014. https://digital.library.unt.edu/ark:/67531/metadc700093/.

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Complex processes whose evolution in time rests on the occurrence of a large and random number of intermittent events are the systems under study. The mean time distance between two consecutive events is infinite, thereby violating the ergodic condition and activating at the same time a stochastic central limit theorem that explains why the Mittag-Leffler function is a universal property of nature. The time evolution of these complex systems is properly generated by means of fractional differential equations, thus leading to the interpretation of fractional trajectories as the average over many random trajectories, each of which fits the stochastic central limit theorem and the condition for the Mittag-Leffler universality. Additionally, the effect of noise on the generation of the Mittag-Leffler function is discussed. Fluctuations of relatively weak intensity can conceal the asymptotic inverse power law behavior of the Mittag-Leffler function, providing a reason why stretched exponentials are frequently found in nature. These results afford a more unified picture of complexity resting on the Mittag-Leffler function and encompassing the standard inverse power law definition.
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Humphreys, Natalia A. "A central limit theorem for complex-valued probabilities /." The Ohio State University, 1999. http://rave.ohiolink.edu/etdc/view?acc_num=osu1488187049540163.

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Zhang, Na. "Limit Theorems for Random Fields." University of Cincinnati / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1563527352284677.

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Mok, Kit Ying. "Central limit theorem for nonparametric regression under dependent data /." View Abstract or Full-Text, 2003. http://library.ust.hk/cgi/db/thesis.pl?MATH%202003%20MOK.

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Rahman, Mohammad Mahbubur. "Central Limit Theorem for some classes of dynamical systems." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp04/mq25986.pdf.

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Thangavelu, Karthinathan. "Quantile estimation based on the almost sure central limit theorem." Doctoral thesis, [S.l.] : [s.n.], 2006. http://webdoc.sub.gwdg.de/diss/2006/thangavelu.

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Books on the topic "Central limit theorem"

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Paulauskas, V., and A. Račkauskas. Approximation Theory in the Central Limit Theorem. Dordrecht: Springer Netherlands, 1989. http://dx.doi.org/10.1007/978-94-011-7798-6.

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Fischer, Hans. A History of the Central Limit Theorem. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-0-387-87857-7.

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Fernandes, Marcelo. Central limit theorem for asymmetric kernel functionals. Florence: European University Institute, 2000.

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Fernandes, Marcelo. Central limit theorem for asymmetric kernel functionals. Badia Fiesolana, San Domenico: European University Institute, 2000.

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Jong, Peter de. Central limit theorems for generalized multilinear forms. [Amsterdam, the Netherlands]: Centrum voor Wiskunde en Information, 1989.

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Adams, William J. The life and times of the central limit theorem. 2nd ed. Providence, R.I: American Mathematical Society, 2009.

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Adams, William J. The life and times of the central limit theorem. 2nd ed. Providence, R.I: American Mathematical Society, 2009.

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Adams, William J. The life and times of the central limit theorem. 2nd ed. Providence, R.I: American Mathematical Society, 2009.

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Jurek, Zbigniew J. Operator-limit distributions in probability theory. New York: Wiley, 1993.

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Senatov, V. V. Qualitative effects in the estimates of the convergence rate in the central limit theorem in multidimensional spaces. Moscow: Maik Nauka/Interperiodica Publishing, 1996.

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Book chapters on the topic "Central limit theorem"

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Rossman, Allan J., and Beth L. Chance. "Central Limit Theorem." In Workshop Statistics, 263–75. New York, NY: Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4757-2926-9_16.

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Gooch, Jan W. "Central Limit Theorem." In Encyclopedic Dictionary of Polymers, 971–72. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4419-6247-8_15172.

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Dedecker, Jérôme, Paul Doukhan, Gabriel Lang, León R. José Rafael, Sana Louhichi, and Clémentine Prieur. "Central Limit theorem." In Weak Dependence: With Examples and Applications, 153–97. New York, NY: Springer New York, 2007. http://dx.doi.org/10.1007/978-0-387-69952-3_7.

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Deshmukh, Shailaja R., and Akanksha S. Kashikar. "Central Limit Theorem." In Probability Theory, 430–78. Boca Raton: Chapman and Hall/CRC, 2024. http://dx.doi.org/10.1201/9781032619057-10.

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Jacod, Jean, and Philip Protter. "The Central Limit Theorem." In Universitext, 181–88. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-642-55682-1_21.

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Roe, Byron P. "The Central Limit Theorem." In Probability and Statistics in Experimental Physics, 90–101. New York, NY: Springer New York, 1992. http://dx.doi.org/10.1007/978-1-4757-2186-7_10.

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Gorban, Igor I. "The Central Limit Theorem." In The Statistical Stability Phenomenon, 261–70. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-43585-5_19.

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Simonnet, Michel. "The Central Limit Theorem." In Measures and Probabilities, 326–43. New York, NY: Springer New York, 1996. http://dx.doi.org/10.1007/978-1-4612-4012-9_16.

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Dekking, Frederik Michel, Cornelis Kraaikamp, Hendrik Paul Lopuhaä, and Ludolf Erwin Meester. "The central limit theorem." In A Modern Introduction to Probability and Statistics, 195–205. London: Springer London, 2005. http://dx.doi.org/10.1007/1-84628-168-7_14.

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Roe, Byron P. "The Central Limit Theorem." In Probability and Statistics in Experimental Physics, 107–18. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4684-9296-5_11.

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Conference papers on the topic "Central limit theorem"

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Frieden, B. Roy. "An optical central limit theorem." In Frontiers in Optics. Washington, D.C.: OSA, 2003. http://dx.doi.org/10.1364/fio.2003.thmm5.

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HORA, AKIHITO, and NOBUAKI OBATA. "QUANTUM DECOMPOSITION AND QUANTUM CENTRAL LIMIT THEOREM." In Proceedings of the Japan-Italy Joint Workshop on Quantum Open Systems, Quantum Chaos and Quantum Measurement. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812704412_0016.

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Li, Jiange, Arnaud Marsiglietti, and James Melbourne. "Entropic Central Limit Theorem for Rényi Entropy." In 2019 IEEE International Symposium on Information Theory (ISIT). IEEE, 2019. http://dx.doi.org/10.1109/isit.2019.8849533.

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Bauer, D., M. Deistler, and W. Scherrer. "A central limit theorem for subspace algorithms." In 1997 European Control Conference (ECC). IEEE, 1997. http://dx.doi.org/10.23919/ecc.1997.7082619.

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Sharipov, Sadillo O. "Central limit theorem for branching process with immigration." In INTERNATIONAL UZBEKISTAN-MALAYSIA CONFERENCE ON “COMPUTATIONAL MODELS AND TECHNOLOGIES (CMT2020)”: CMT2020. AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0057214.

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Fitrianto, Anwar, and Imam Hanafi. "Exploring central limit theorem on world population density data." In INTERNATIONAL CONFERENCE ON QUANTITATIVE SCIENCES AND ITS APPLICATIONS (ICOQSIA 2014): Proceedings of the 3rd International Conference on Quantitative Sciences and Its Applications. AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4903664.

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Formanov, Shakir, Bikajon Khusainova, and Abdulhamid Sirozhitdinov. "On the numerical characteristics in the central limit theorem." In INTERNATIONAL UZBEKISTAN-MALAYSIA CONFERENCE ON “COMPUTATIONAL MODELS AND TECHNOLOGIES (CMT2020)”: CMT2020. AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0058101.

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Gavalakis, Lampros, and Ioannis Kontoyiannis. "The Entropic Central Limit Theorem for Discrete Random Variables." In 2022 IEEE International Symposium on Information Theory (ISIT). IEEE, 2022. http://dx.doi.org/10.1109/isit50566.2022.9834855.

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Horbacz, Katarzyna. "The central limit theorem for continuous random dynamical systems." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2016). Author(s), 2017. http://dx.doi.org/10.1063/1.4992709.

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Ke, Liu, Ren Xiang, and Jiang Huanjun. "Almost sure central limit theorem on maxima and minima." In 2011 International Conference on Mechatronic Science, Electric Engineering and Computer (MEC). IEEE, 2011. http://dx.doi.org/10.1109/mec.2011.6025877.

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Reports on the topic "Central limit theorem"

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Rachev, S. T., and J. E. Yukich. Convolution Metrics and Rates of Convergence in the CLT (Central Limit Theorem). Fort Belvoir, VA: Defense Technical Information Center, October 1987. http://dx.doi.org/10.21236/ada189341.

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Wright, T. Central limit theorem for variable size simple random sampling from a finite population. Office of Scientific and Technical Information (OSTI), February 1986. http://dx.doi.org/10.2172/6138951.

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Li, Deli, M. B. Rao, and R. J. Tomkins. The Law of the Iterated Logarithm and Central Limit Theorem for L-Statistics. Fort Belvoir, VA: Defense Technical Information Center, July 1997. http://dx.doi.org/10.21236/ada328387.

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Adler, Robert J., and R. Epstein. A Central Limit Theorem for Markov Paths and Some Properties of Gaussian Random Fields. Fort Belvoir, VA: Defense Technical Information Center, February 1986. http://dx.doi.org/10.21236/ada170258.

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Chetverikov, Denis, Victor Chernozhukov, and Kengo Kato. Central limit theorems and bootstrap in high dimensions. IFS, December 2014. http://dx.doi.org/10.1920/wp.cem.2014.4914.

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Kato, Kengo, Victor Chernozhukov, and Denis Chetverikov. Central limit theorems and bootstrap in high dimensions. The IFS, August 2016. http://dx.doi.org/10.1920/wp.cem.2016.3916.

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Chaganty, N. R., and J. Sethuraman. Central Limit Theorems in the Area of Large Deviations for Some Dependent Random Variables. Fort Belvoir, VA: Defense Technical Information Center, January 1985. http://dx.doi.org/10.21236/ada153125.

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Chernozhukov, Victor, Denis Chetverikov, and Kengo Kato. Central limit theorems and multiplier bootstrap when p is much larger than n. Institute for Fiscal Studies, December 2012. http://dx.doi.org/10.1920/wp.cem.2012.4512.

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Nearly optimal central limit theorem and bootstrap approximations in high dimensions. Cemmap, March 2021. http://dx.doi.org/10.47004/wp.cem.2021.0821.

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