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Exploring α-ψ-ϕ contractive mapping: novel fixed point theorems in complete b-metric spaces. [PDF]
Raji T +6 more
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Hawking-Type Singularity Theorems for Worldvolume Energy Inequalities. [PDF]
Graf M +3 more
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On the Lin Condition in Strong Ratio Limit Theorems
Mathematical Notes, 2004Let \((X_n,n\geq 0)\) be a Markov chain with state space \((E,{\mathcal B})\) and \(P\) be a transition operator. It is proved that for a wide class of Markov chains and, in particular, for many random walks on groups the formula (Lin condition) \(\liminf (v(P^{n+1}f)/ v(P^nf))=1\) holds, where \(v\) and \(f\) are a probability measure on \({\mathcal B}
M G Shur
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On strong versions of the central limit theorem
Statistics & Probability Letters, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Rychlik, Zdzisław, Szuster, Konrad S.
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A Strong Limit Theorem on Random Selection
Southeast Asian Bulletin of Mathematics, 2002The idea of random selection on gambling systems has been extended to Markov chains using the notion of likelihood ratio and an analytic technique. A strong limit theorem on the relative frequency of ordered couple under random selection has been established.
Shi, Yimin, Xu, Yong, Kang, Huiguang
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Strong Limit Theorems in Noncommutative L2-Spaces
Lecture Notes in Mathematics, 1991Ryszard Jajte
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On Strong Versions of the Central Limit Theorem
Mathematische Nachrichten, 1988AbstractLet Sn be the sum of n i.i.d.r.v. and let 1(‐∞,x)(·) be the indicator function of the interval (‐∞, x). Then the sequence 1(‐∞, x)(Sn/√n) does not converge for any x. Likewise the arithmetic means of this sequence converge only with probability zero. But the logarithmic means converge with probability one to the standard normal distribution Ø(x)
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