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Strong limit theorems for random fields

, 2011
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On the Lin Condition in Strong Ratio Limit Theorems

Mathematical Notes, 2004
Let \((X_n,n\geq 0)\) 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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Strong limit theorems for arbitrary stochastic sequences [PDF]

Journal of Mathematical Analysis and Applications, 2007
In this paper, we establish two strong limit theorems for arbitrary stochastic sequences.
Weiguo Yang
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Strong ratio limit theorems

Lecture Notes in Mathematics, 1983
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On strong versions of the central limit theorem

Statistics & Probability Letters, 2003
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Rychlik, Zdzisław, Szuster, Konrad S.
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A Strong Limit Theorem on Random Selection

Southeast Asian Bulletin of Mathematics, 2002
The 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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On Strong Versions of the Central Limit Theorem

Mathematische Nachrichten, 1988
AbstractLet 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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The Work of A. N. Komogorov on Strong Limit Theorems

Theory of Probability & Its Applications, 1990
See the review in Zbl 0662.60045.
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Strong Limit Theorems for Increments of Renewal Processes

Journal of Mathematical Sciences, 2005
Let \(X_i\), \(i\geq 1\), be i.i.d. nonnegative nondegenerate random variables with \(\text{ess\,inf\,}X_1= 0\), \(0< EX_1=\mu a_T\). The main theorems show that under moderate conditions \(\limsup W_T/b_T= \limsup(u_T- a_T/\mu)= \limsup u_T/b_T= 1\), a.s. and even lim instead of lim\,sup.
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One-Sided Versions of Strong Limit Theorems

Theory of Probability & Its Applications, 1984
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