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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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SIMULATED ANNEALING FOR ALMOST SURE CONVERGENT RANDOM SEQUENCES

Statistics & Risk Modeling, 2001
Summary: A stochastic simulated annealing algorithm is defined in order to find solutions to a minimization problem connected with a function defined on a finite set which is the almost sure limit of a sequence of random variables. The convergence to equilibrium of the algorithm is shown and the asymptotic properties of the sequence of equilibrium ...
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On almost sure convergence of asymptotic martingales

1993
Summary: The aim of this paper is to give a characterization of almost sure convergence for sequences of random variables, which do not necessarily have first moments. An example of such characterization was given by \textit{I. A. Dzhvarsheishvili} [Theory Probab. Appl. 33, 260-269 (1988)], where a notion of a \(D_v\)-amart was introduced. We show that
Kruk, Łukasz, Zięba, Wiesław (1950- )
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Regularity and almost sure convergence

1995
Summary: We give a sufficient condition for almost sure convergence in the sense of \textit{E. Hensz} and \textit{R. Jajte} [Math. Z. 193, 413-429 (1986; Zbl 0613.46056)] to be equivalent to almost uniform convergence.
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Almost sure convergence of projections in \(L_p\)-spaces

1997
Summary: The paper is devoted to the analysis of pointwise convergence of sequences of projections in \(L_p\)-spaces. Also some approximation problems for operators in \(L_2\)-spaces are discussed.
Hensz-Chądzyńska, Ewa   +2 more
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Almost Sure Convergence of Multi-Indexed Series

2014
One of the fundamental results of the classical probability theory is the so-called Kolmogorov three series theorem.
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