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On Some Limit Theorems of Probability Theory
Theory of Probability & Its Applications, 1960The following problem is considered in the paper. Let\[ \xi _{n,1} ,\xi _{n,2} , \cdots ,\xi _{n,kn} ,\quad n = 1,2, \cdots , \] be a sequence of a series of independent random variables; $\varphi ...
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Convergence of Random Processes and Limit Theorems in Probability Theory
Theory of Probability & Its Applications, 1956The convergence of stochastic processes is defined in terms of the so-called “weak convergence” (w. c.) of probability measures in appropriate functional spaces (c. s. m. s.).Chapter 1. Let $\Re $ be the c.s.m.s. and v a set of all finite measures on $\Re $.
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B.V. Gnedenko: Classic of Limit Theorems in the Theory of Probability
Methodology and Computing in Applied Probability, 2013This paper deals with an analysis of mathematical contributions of the mathematician B. V. Gnedenko, who worked in the area of probability theory and its applications. He created in Ukraine a worldwide-known school of probability theory and mathematical statistics and influenced the formation of theoretical-probabilistic schools in many countries.
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On the Central Limit Theorem of Probability Theory
2015In an earlier paper,\(^1\) among other results, exact conditions were determined for the classical Laplace-Ljapounoff limit theorem to hold, and a criterion was given to determine whether a given sequence of distribution functions converges to the Gaussian standard normal distribution function \(\Phi (x)\) (in which case one could also calculate both ...
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On The Limit Theorems of Probability Theory
1992As is well known, the fundamental ideas of P. Laplace [1] and P.L. Chebyshev [2] were subsequently developed in papers by A.A. Markov [3] and A.M. Lyapunov [4], culminating in a very general statement (the so-called Lyapunov theorem) on the limit of probability distributions for sums of a large number of small independent random variables.
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Limit Theorems of Probability Theory.
Journal of the American Statistical Association, 1976P. K. Sen, P. Revesz
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A Proof of the Generalized Second-Limit Theorem in the Theory of Probability
Communications in Statistics - Theory and Methods, 2011Some theorems of q-additive and q-multiplicative functions are presented, where the summation is taken over some arithmetically interesting subsets of the integers.
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Limit Theorems of Probability Theory.
Journal of the Royal Statistical Society. Series A (General), 1977John Haigh, P. Revesz
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Eventologically multivariate extensions of probability theory’s limit theorems [PDF]
, 2009 Eventologically multivariate extensions of probability theory’s limit theorems are proposed. Eventologically multivariate version of limit theorems extends its classical probabilistic interpretation and involves into its structure of dependencies of arbitrary set of events which appears in sequence of independent tests.
Vorobyev, Oleg Yu. +1 more
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