Results 261 to 270 of about 11,838 (304)

ALMOST SURE CONVERGENCES IN THE LAW OF LARGE NUMBERS

Journal of the London Mathematical Society, 2003
Summary: The integrability of a control function of the almost sure convergence \[ \lim_{n\to\infty} \frac{X_1(\omega)+ X_2 (\omega+ \cdots+X_n (\omega)}{T_n}, \] where \(T_n\uparrow\infty\) as \(n\to\infty\) and \(X_1,X_2,\dots,X_n,\dots\) are independent identically distributed random variables, is studied.
KAORU YONEDA, Shigeru Takahashi
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On the convergence of bivariate order statistics: Almost sure convergence and convergence rate

Journal of Computational and Applied Mathematics, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Anshui Li, Yuanyuan Wang, Minzhi Zhao
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On $(B,\rho )$-Amarts and Almost Sure Convergence

Theory of Probability & Its Applications, 1996
The main aim of this paper is to generalize a conditional amart [\textit{D. Szynal} and the second author, Bull. Pol. Acad. Sci., Math. 34, 635-642 (1986; Zbl 0615.60027), the second author, Theory Probab. Appl. 36, No. 3, 637-639 (1991) and Teor. Veroyatn. Primen. 36, No. 3, 616-617 (1991; Zbl 0739.60036)] and a \(D_v\)-amart [\textit{I.
Kruk, L., Ziȩba, W.
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Almost Sure Convergence

2012
This chapter studies essentially Strong Laws of Large Numbers (SLLN) for associated variables and their applications to the characterization of asymptotics of statistical estimators under associated sampling. It is possible to prove SLLN under fairly general assumptions, but, in order to prove characterizations of convergence rates, a closer care on ...
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Convergence Almost Surely and in Probability

1989
In this lesson we look at some theorems on convergence of sequences of numerical (extended real) valued functions. All will be used at some point later particularly in the lessons on integration. We keep a fixed [ΩSP].
Hung T. Nguyen, Gerald S. Rogers
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Summability methods and almost sure convergence

Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1985
The authors investigate almost sure convergence for sequences of i.i.d. random variables under different methods of summability. We say \(s_ n\to s\) (P), if \(\sum^{\infty}_{j=0}s_ jP(S_ n=j)\to s\) as \(n\to \infty\), where \(S_ n:=\xi_ 1+...+\xi_ n\), and \(\xi_ 1,\xi_ 2,..\). are integer-valued independent random variables.
Bingham, N. H., Maejima, Makoto
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Almost Sure Convergence

2017
This chapter gives the basic theory of almost sure convergence and Kolmogorov’s strong law of large numbers (1933) according to which the empirical mean of an iid sequence of integrable random variables converges almost surely to the probabilistic mean (the expectation).
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Convergence: Almost Surely and in Probability

1996
For nets of maps defined on a single, fixed probability space (Ω, A, P), convergence almost surely and in probability are frequently used modes of stochastic convergence, stronger than weak convergence. In this section we consider their nonmeasurable extensions together with the concept of almost uniform convergence, which is equivalent to outer almost
Aad W. van der Vaart, Jon A. Wellner
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Almost sure convergence for stochastic integrals

Commentarii mathematici Universitatis Sancti Pauli = Rikkyo Daigaku sugaku zasshi, 1988
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Almost Sure Convergence of Delayed Renewal Processes

Journal of the London Mathematical Society, 1987
Consider a renewal process \(\{N(t)\}_{t\geq 0}\) associated with a sequence \(\{X_ i\}_{i=1,2,...}\) of nonnegative and independent, identically distributed ''failure times''. Appropriate generalized moment conditions are presented which are necessary and sufficient for certain law of iterated logarithm type results on the ''delayed renewal process'',
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