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Convergence Almost Surely and in Probability
1989In 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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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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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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ALMOST SURE CONVERGENCES IN THE LAW OF LARGE NUMBERS
Journal of the London Mathematical Society, 2003Summary: 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 $(B,\rho )$-Amarts and Almost Sure Convergence
Theory of Probability & Its Applications, 1996The 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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Summability methods and almost sure convergence
Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1985The 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 for stochastic integrals
Commentarii mathematici Universitatis Sancti Pauli = Rikkyo Daigaku sugaku zasshi, 1988zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Almost Sure Convergence of Delayed Renewal Processes
Journal of the London Mathematical Society, 1987Consider 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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On the almost sure convergence of Syracuse sequences
Statistics & Probability Letters, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Slakmon, Alain, Macot, Luc
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Epi-convergence almost surely, in probability and in distribution
Annals of Operations Research, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Almost sure convergence of the Hill estimator
Mathematical Proceedings of the Cambridge Philosophical Society, 1988AbstractIn this note we characterize those sequencesknsuch that the Hill estimator of the tail index based on theknupper order statistics of a sample of sizenfrom a Pareto-type distribution is strongly consistent.
Deheuvels, Paul +2 more
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