Rozprawy doktorskie na temat „Conditionally independent random variables”
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Vuong, Christophe. "Contributions to stochastic analysis for non-diffusive structures". Electronic Thesis or Diss., Institut polytechnique de Paris, 2023. http://www.theses.fr/2023IPPAT054.
Pełny tekst źródłaThis thesis is concerned with the study of non-diffusive structures. We focus on two classes of such structures.The first subject deals with Malliavin calculus for conditionally independent random variables, which is a special case of discrete Malliavin calculus. It also generalizes the calculus that has been developed for countable products of probability spaces, for independent random variables.In our case, the interest of such a calculus is to complement results in stochastic analysis with proofs of functional inequalities (Poincaré inequality, McDiarmid's inequality) and limit theorems. One of the main applications is the determination of the convergence rate of central limit theorems via the Stein method.By combining Malliavin calculus with the underlying Dirichlet structure of the random variables, we obtain an integration by parts formula which is key to the derivations of so-called Stein bounds of the rates of convergence. We show quantitative limit theorems, including a fourth moment theorem with remainder. In particular, we discuss an application to the asymptotic normality of motif counting in exchangeable random hypergraphs.The second subject studies functionals of a Poisson measure using the notion of invertibility of transformations of that measure on the sample space of random measures. We use the identification of these measures and the associated marked point processes. Invertible transformations are obtained via the Girsanov's theorem, respecting absolute continuity with respect to the reference measure. This results in an entropy criterion for the invertibility of transformations. Finally, we make the connection with stochastic differential equations driven by Poisson measures
Kasparavičiūtė, Aurelija. "Theorems of large deviations for the sums of a random number of independent random variables". Doctoral thesis, Lithuanian Academic Libraries Network (LABT), 2014. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2014~D_20140121_101308-41106.
Pełny tekst źródłaDisertacinio darbo tyrimo objektas yra atsitiktinio dėmenų skaičiaus nepriklausomų vienodai pasiskirsčiusių atsitiktinių dydžių su teigiamais svoriniais koeficientais sumos, kurios kaip modelis sutinkamos, pavyzdžiui, finansų, draudos matematikose. Daromos prielaidos, kad atsitiktinis dėmenų skaičius yra nepriklausomas nuo sumos dėmenų, atsitiktiniai dėmenys tenkina apibendrintą S. N. Bernšteino sąlygą, o atsitiktinis dėmenų skaičius kartu su svoriais tenkina tam tikras suderinamumo sąlygas. Disertacijos tikslas yra standartizuotos (centruotos ir normuotos) minėtos atsitiktinės sumos skirstinio aproksimacija standartiniu normaliuoju dėsniu didžiųjų nuokrypių tiek Kramero, tiek ir laipsninėse Liniko zonose.
Sambale, Holger [Verfasser]. "Second order concentration for functions of independent random variables / Holger Sambale". Bielefeld : Universitätsbibliothek Bielefeld, 2016. http://d-nb.info/1084888173/34.
Pełny tekst źródłaWu, Hao-cun. "Independent component analysis and its applications in finance". Click to view the E-thesis via HKUTO, 2007. http://sunzi.lib.hku.hk/HKUTO/record/B39559099.
Pełny tekst źródła吳浩存 i Hao-cun Wu. "Independent component analysis and its applications in finance". Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2007. http://hub.hku.hk/bib/B39559099.
Pełny tekst źródłaBaumgarten, Christoph [Verfasser], i Frank [Akademischer Betreuer] Aurzada. "Persistence of sums of independent random variables, iterated processes and fractional Brownian motion / Christoph Baumgarten. Betreuer: Frank Aurzada". Berlin : Universitätsbibliothek der Technischen Universität Berlin, 2013. http://d-nb.info/1035276445/34.
Pełny tekst źródłaPaditz, Ludwig. "Über die Annäherung von Summenverteilungsfunktionen gegen unbegrenzt teilbare Verteilungsfunktionen in der Terminologie der Pseudomomente". Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-112967.
Pełny tekst źródłaThe pseudo-moments serve as a characteristic of the approach of the components of a cumulative distribution function to the components of the limit distribution function. In the terminology of pseudo-moments estimates of the approximation of the cumulative distribution function by an indefinite divisible distribution function can be specified. The results are derived without the assumption of the so-called condition of infinitesimality. There are given some estimations with or without the assumption of finite variances. Finally some references are given
Bacro, Jean-Noël. "Sur les accroissements des processus de sommes partielles de variables aléatoires indépendantes". Paris 6, 1986. http://www.theses.fr/1986PA066372.
Pełny tekst źródłaHalconruy, Hélène. "Calcul de Malliavin et structures de Dirichlet pour des variables aléatoires indépendantes". Electronic Thesis or Diss., Institut polytechnique de Paris, 2020. http://www.theses.fr/2020IPPAT016.
Pełny tekst źródłaMalliavin calculus was initially developed to provide an infinite-dimensional variational calculus on the Wiener space and further extended to other spaces. In this work, we develop such one in two discrete frameworks. First, we equip any countable product of probability spaces with a discrete Dirichlet-Malliavin structure, consisting of a family of Malliavin operators (gradient, divergence, number operator), an integration by parts formula, and the induced Dirichlet forms. We get the analogues of the classical functional identities and retrieve the usual Poisson and Brownian Dirichlet structures as limits of our induced structures. We provide discrete Stein-Malliavin criterions for the Normal and the Gamma approximations. Second we study insider's trading in a ternary model, Iying on a three-points compound geometric process. We state a modified chaotic decomposition and define the geometric gradient and divergence operators as the annihilation and creation operators acting on it. We state a geometric Ocone-Karatzas formula. We express the insider's additional expected logarithmic utility in terms of relative entropy as in the continuous case
Paditz, Ludwig. "Über mittlere Abweichungen". Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-112977.
Pełny tekst źródłaIn this paper we study necessary and sufficient conditions for the validity of limit theorems on moderate deviations. Usually x-zones for moderate deviations are called in the terminilogy by YU.V.LINNIK (1971) "very narrow" zones of integral normal attraction. Moreover we analyse the remainder term appearing in the asymptotic relations. Informations on the order of the rate of convergence are given. Earlier results by several authors are generalized. Finally some references are given
Paditz, Ludwig. "Über die Annäherung der Verteilungsfunktionen von Summen unabhängiger Zufallsgrößen gegen unbegrenzt teilbare Verteilungsfunktionen unter besonderer Beachtung der Verteilungsfunktion der standardisierten Normalverteilung". Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-114206.
Pełny tekst źródłaWith the presented work new contributions to basic research in the field of limit theorems of probability theory are given. Limit theorems for sums of independent random variables taking on the most diverse lines of research in probability theory an important place in modern times and are no longer only of theoretical interest. In the work results are presented to newer problems on the summation theory of independent random variables, at first time in the fifties and sixties of the 20th Century appeared in the literature and have been studied in the past few years with great interest. International two main directions have emerged in the theory of limit theorems: Firstly, the questions on the convergence speed of a cumulative distribution function converges to a predetermined limit distribution function, and on the other hand the questions on an error estimate for the limit distribution function at a finite summation process. First indefinite divisible limit distribution functions are considered, then the normal distribution is specifically discussed as a limit distribution. As characteristic parameters both moments or one-sided moments or pseudo-moments are used. The error estimates are stated both in uniform as well as non-uniform residual bounds including a description of the occurring absolute constants. Both the method of characteristic functions as well as direct methods (convolution method) can be further expanded as proof methods. Now for the error estimate, 1965 given by Bikelis, was the first time to estimate the appearing absolute constant C with C = 114.667 numerically. Furthermore, in the work of so-called limit theorems for moderate deviations are studied. Here also remainder estimates are derived for the first time. In recent years to the proof of limit theorems the chosen way of the convolution of distribution functions proved to be groundbreaking and determined the development of both the theory of limit theorems for moderate and large deviations as well as the investigation into the nonuniform estimates in the central limit theorem significantly. The convolution method is in the present thesis, the main instrument of proof. Thus, it was possible to obtain a series of results and obtain new numerical results in particular by means of electronic data processing
Paditz, Ludwig. "Über eine Fehlerabschätzung im zentralen Grenzwertsatz". Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-112986.
Pełny tekst źródłaWe consider a sequence of centered and independent random variables with moments of order m, 2
Paditz, Ludwig. "Abschätzungen der Konvergenzgeschwindigkeit im zentralen Grenzwertsatz". Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-112958.
Pełny tekst źródłaThe paper is a generalization of the results, published by the author in Informationen/07; 1976,05. Let F_n(x) be the cdf of X_1+X_2+...+X_n, where X_1, X_2, ...,X_n are non iid random variables with m-th absolute moment c_m, m>2, and Phi the cdf of the unit normal law. Explicit universal constants L_m are computed such that we have some error estimates in the nonuniform central limit theorem. A special case is the nonuniform error bound by A.BIKELIS (1966) in the case of existence of third absolute moments. Furthermore limit theorems with assumption of onesided moments are considered. Some references are given
Paditz, Ludwig. "Beiträge zur expliziten Fehlerabschätzung im zentralen Grenzwertsatz". Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-115105.
Pełny tekst źródłaIn the work the asymptotic behavior of suitably centered and normalized sums of random variables is investigated, which are either independent or occur in the case of dependence as a sequence of martingale differences or a strongly multiplicative system. In addition to the classical theory of summation limiting processes are considered with an infinite summation matrix or an adapted sequence of weighting functions. It will be further developed the method of characteristic functions, and especially the direct method of the conjugate distribution functions to prove quantitative statements about uniform and non-uniform error estimates of the remainder term in central limit theorem. The investigations are realized in the Lp metric, 1
Paditz, Ludwig. "Abschätzungen der Konvergenzgeschwindigkeit zur Normalverteilung unter Voraussetzung einseitiger Momente (Teil 1)". Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-112930.
Pełny tekst źródłaThe paper is divided in two parts: part 1 (cp. Informationen/07; 1976,05) and part 2 (cp. Informationen/07; 1976,06). Part 1 contains an introduction and limit theorems for iid random variables and the transfer of the considered limit theorems to the case of the existence of onesided moments. Part 2 contains limit theorems of moderate deviations for sums of series of non iid random variables and a discussion of all obtained results in part 1 and 2 and finally some references. Let F_n(x) be the cdf of X_1+X_2+...+X_n, where X_1, X_2, ...,X_n are iid random variables with mean 0 and variance 1 and with m-th absolute moment c_m, m>2, and Phi the cdf of the unit normal law. Explicit universal constants L_i are computed such that we have an error estimate in the nonuniform central limit theorem with the L_i, where i corresponds to the five cases considered: small x, moderate deviations for x, large deviations for x, small n , large n. Additional upper bounds for 1-F_n(x) are obtained if the one-sided moments of order m, m>2, are finite and if x>D_m*n^(1/2)*ln(n) and x>D_m*n^(1/2)*(ln(n))^(1/2) respectively improving results by S.V.NAGAEV (1965)
Paditz, Ludwig. "Abschätzungen der Konvergenzgeschwindigkeit zur Normalverteilung unter Voraussetzung einseitiger Momente (Teil 2)". Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-112947.
Pełny tekst źródłaThe paper is divided in two parts: part 1 (cp. Informationen/07; 1976,05) and part 2 (cp. Informationen/07; 1976,06). Part 1 contains an introduction and limit theorems for iid random variables and the transfer of the considered limit theorems to the case of the existence of onesided moments. Part 2 contains limit theorems of moderate deviations for sums of series of non iid random variables and a discussion of all obtained results in part 1 and 2 and finally some references. Let F_n(x) be the cdf of X_1+X_2+...+X_n, where X_1, X_2, ...,X_n are iid random variables with mean 0 and variance 1 and with m-th absolute moment c_m, m>2, and Phi the cdf of the unit normal law. Explicit universal constants L_i are computed such that we have an error estimate in the nonuniform central limit theorem with the L_i, where i corresponds to the five cases considered: small x, moderate deviations for x, large deviations for x, small n , large n. Additional upper bounds for 1-F_n(x) are obtained if the one-sided moments of order m, m>2, are finite and if x>D_m*n^(1/2)*ln(n) and x>D_m*n^(1/2)*(ln(n))^(1/2) respectively improving results by S.V.NAGAEV (1965)
Silva, Mariana Barbosa da. "Estimadores do tipo n?cleo para Vari?vei s I.I.D. com espa?o de estados geral". Universidade Federal do Rio Grande do Norte, 2012. http://repositorio.ufrn.br:8080/jspui/handle/123456789/17011.
Pełny tekst źródłaCoordena??o de Aperfei?oamento de Pessoal de N?vel Superior
In this work, the paper of Campos and Dorea [3] was detailed. In that article a Kernel Estimator was applied to a sequence of random variables with general state space, which were independent and identicaly distributed. In chapter 2, the estimator?s properties such as asymptotic unbiasedness, consistency in quadratic mean, strong consistency and asymptotic normality were verified. In chapter 3, using R software, numerical experiments were developed in order to give a visual idea of the estimate process
Neste trabalho estudamos um dos m?todos n?o-param?trico: os Estimadores do Tipo N?cleo associado a uma sequ?ncia de vari?veis aleat?rias independentes e identicamente distribu?das com espa?o de estados geral, mais precisamente o trabalho de Campos e Dorea [3]. No Cap?tulo 2 verificamos as boas qualidades dessa classe de estimadores como n?o v?cio assint?tico, converg?ncia em m?dia quadr?tica, consist?ncia forte e normalidade assint?tica. No Cap?tulo 3 com o auxilio do software R temos uma id?ia visual do que ocorre no processo de estima??o
黃彥青. "PAIRWISE INDEPENDENT RANDOM VARIABLES". Thesis, 2001. http://ndltd.ncl.edu.tw/handle/47864460351789081997.
Pełny tekst źródła國立中央大學
數學研究所
89
Abstract Pairwise independence is not enough for the central limit theorem to hold. In my thesis, some related results are mentioned. I also give some new version of conditions such that the central limit theorem would hold for pairwise independent sequences. Finally, I give an example to illustrate the results.
Shiu, Shang-Yuan, i 須上苑. "A Study of Complete Convergence for sequences of Independent Random Variables". Thesis, 2002. http://ndltd.ncl.edu.tw/handle/37694870443392204530.
Pełny tekst źródłaSzuma, Pei-Wen, i 司馬佩文. "On Asymptotics of Order Statistics in Independent Nonidentically Distributed Random Variables". Thesis, 1996. http://ndltd.ncl.edu.tw/handle/31842658859576475036.
Pełny tekst źródła國立中山大學
應用數學研究所
84
Let {X_n, n>= 1} be a sequence of independent random variables with continuous distribution functions {F_n, n>= 1}, and X_{[1: n]}<= X_{[2:n]}<= ... <= X_{[n:n]} be the corresponding order statistics for sample size n. For every k (1<= k <= n), let F_{kn} denote the distribution function of X_{[k:n]} and M_n= max{X_1,...,X_n}. For this work, when {F_n, n>= 1} come from some special families with certain parameters, we are interested in finding some conditions for those parameters to determine $a_n$ and $b_n$ such that F_{nn}(a_nx+b_n) converges to a nondegenerate distribution. When {F_n, n>= 1} come from general families, we also find some conditions for {F_n, n>= 1}, a_n and b_n such that F_{kn}(a_nx+b_n) converges to standard Normal distribution, where k=qn, q in (0,1).
Hsu, Shih-Yi, i 許世易. "The Rate of Complete Convergence for 2m Independent and Identical Distributed Random Variables". Thesis, 1999. http://ndltd.ncl.edu.tw/handle/17501214365158068459.
Pełny tekst źródłaYu, Po-Chuan, i 游伯銓. "Law of the large numbers and probability inequalities for the independent random variables". Thesis, 1994. http://ndltd.ncl.edu.tw/handle/52106970328366021182.
Pełny tekst źródła淡江大學
數學系
82
The techniques and the relative mathematical devices for proving the strong law of large numbers (S.L.L.N.) are studied in the thesis. We discuss how to slve the almost sure (a.s.) convergence problems of the sequence of partial sum. That is to deal with the S.L.L.N. The fundamental methods for proving the S.L.L.N. are surveyed in chapter 1. For understanding the application of the fundamental methods, the fundamental methods are used to prove Borel's S.L.L.N.By virtue of this study process, we will have a better and widespread understanding of the allied mathematical devicse for proving S.L.L.N. 4 fundamental methods for proving S.L.N.N. are collected and discussed. The extensive explorations on the mathematical devices of the above 4 fundamental methods are proposed in chapter 2. For better understanding method 1, we investigate the probability inequalities of partial sum. The curcial step in method 2 is to control the convergence of difference between convergent subsequence and original sequence. Method 3 has relation to the convergence of infinite series. The upper bounds of moment generating functions are explored when fundamental method 4 is used to prove S.S.L.N. the foregoing upper bounds have relation to the Gaussian random variable, so we study the application of the Gaussian random variable. The sufficent and necessary conditions of S.L.L.N. are surveyed in chapter 3 and 4 respectively.
Lin, Yan-Cheng, i 林彥丞. "Convergence Rates in the Law of Large Numbers for 2m Independent and Identically Distributed Random Variables". Thesis, 2002. http://ndltd.ncl.edu.tw/handle/80483115600232551340.
Pełny tekst źródła國立清華大學
數學系
90
Let Xi, i=1…∞ be a sequence of 2m independent and identically distributed random variables . given suitable moment condition ,we are interested in studying the rate of convergence .And we will find out how to choose m .
洪翊書. "A Study On Marcinkiewicz-Zygmund Type Strong Law of Large Numbers for Pairwise Independent Identically Distributed Random Variables". Thesis, 2013. http://ndltd.ncl.edu.tw/handle/75297874249699887452.
Pełny tekst źródłaLiao, yeong-yuan, i 廖永源. "Estimating the number of change points in a sequence of independent normal random variables with unequal means or variances". Thesis, 1996. http://ndltd.ncl.edu.tw/handle/49759045242329099926.
Pełny tekst źródła國立中興大學
應用數學系
84
A simple method is proposed to detect the number of change points in a sequence of independent normal random variables. An estimator to maximize some criterion, saySC(k), which is to maximize the log likelihood function withsome penalty term is used in detection. Under some mild assumptions, the consistency of the estimator for the true number of change points and the boundedness between the estimated change locations and the true change locations are obtained.
Liao, Yong Yuan, i 廖永源. "Estimating the number of change points in a sequence of independent normal random variables with unequal means or variances". Thesis, 1996. http://ndltd.ncl.edu.tw/handle/93180104253872570091.
Pełny tekst źródłaKarlová, Andrea. "Možnosti se stabilními distribucemi". Doctoral thesis, 2013. http://www.nusl.cz/ntk/nusl-327226.
Pełny tekst źródłaPaditz, Ludwig. "Beiträge zur expliziten Fehlerabschätzung im zentralen Grenzwertsatz". Doctoral thesis, 1988. https://tud.qucosa.de/id/qucosa%3A26930.
Pełny tekst źródłaIn the work the asymptotic behavior of suitably centered and normalized sums of random variables is investigated, which are either independent or occur in the case of dependence as a sequence of martingale differences or a strongly multiplicative system. In addition to the classical theory of summation limiting processes are considered with an infinite summation matrix or an adapted sequence of weighting functions. It will be further developed the method of characteristic functions, and especially the direct method of the conjugate distribution functions to prove quantitative statements about uniform and non-uniform error estimates of the remainder term in central limit theorem. The investigations are realized in the Lp metric, 1