Results 281 to 290 of about 51,964 (316)

Almost sure convergence of the forward–backward–forward splitting algorithm

Optimization Letters, 2015
In this paper, we propose a stochastic forward–backward–forward splitting algorithm and prove its almost sure weak convergence in real separable Hilbert spaces. Applications to composite monotone inclusion and minimization problems are demonstrated.
B. Vu
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Almost sure convergence of the multiple ergodic average for certain weakly mixing systems

, 2016
The family of pairwise independently determined (PID) systems, i.e., those for which the independent joining is the only self joining with independent 2-marginals, is a class of systems for which the long standing open question by Rokhlin, of whether ...
Yonatan Gutman, Wen Huang, S. Shao, X. Ye   +3 more
semanticscholar   +1 more source

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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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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Almost sure convergence of sample range

Extremes, 2007
An almost sure limit theorem is derived for the sample range statistics \( R_n=\max_{1\leq i\leq n} X_i-\min_{1\leq i\leq n} X_i \), where \(X_i\) are i.i.d. r.v.s. It states that if for some nonrandom \(\alpha_n\), \(\beta_n\) and some nondegenerate CDF \(G\) \(\zeta_n=\alpha_n(R_n-\beta_n)\) converges in distribution to \(G\) then at any point \(x ...
Zhongquan, Tan, Zuoxiang, Peng, Nadarajah, Saralees   +2 more
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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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Stability bounds and almost sure convergence of improved particle swarm optimization methods

Research in the Mathematical Sciences, 2021
Xin T. Tong, K. P. Choi, T. Lai, W. Wong
semanticscholar   +1 more source

Almost sure convergence and bounded entropy

Israel Journal of Mathematics, 1988
Let (\({\mathcal X},\mu)\) be a probability space, \(S_ n\) a sequence of operators on \(L^ 2(\mu)\), \(\| S_ n\| \leq 1\), \(T_ j\) a sequence of positive isometric operators satisfying \(T_ j(1)=1\), \(J^{-1}\sum_{j\leq J}T_ jf\to \int f d\mu\) \(\forall f\in L^ 1\) and \(T_ jS_ n=S_ nT_ j\).
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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 of branching processes

Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1977
A general theorem concerning the almost sure convergence of some nonhomogeneous Markov chains, whose conditional distributions satisfy a certain convergence condition, is given. This result applied to branching processes with infinite mean yields almost sure convergence for a large class of processes converging in distribution, as well as a ...
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