Results 121 to 130 of about 2,680 (148)

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
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On Strong Limit Theorems for Sums of Independent Random Variables

Theory of Probability & Its Applications, 1993
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Martikaĭnen, A. I., Petrov, V. V.
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Strong limit theorems for anisotropic random walks on ℤ2

Periodica Mathematica Hungarica, 2013
We study the path behaviour of the anisotropic random walk on the two-dimensional lattice ℤ2. Strong approximation of its components with independent Wiener processes is proved. We also give some asymptotic results for the local time in the periodic case.
Endre Csáki, Miklós Csörgo, Antónia Földes, Pál Révész   +3 more
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Uniform Integrability for Strong Ratio Limit Theorems. I

Theory of Probability & Its Applications, 2006
Unlike parts I and II of this paper [Theory Probab. Appl., 50 (2006), pp. 436--447] and [Theory Probab. Appl., 55 (2011), pp. 473--484], which dealt with strong limit theorems for ratios (SLTR) in the traditional sense, now we propose new SLTR with particular parametric sets. The peculiarity of these theorems is that their statements ignore some values
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On a local limit theorem in strong sense

Statistics & Probability Letters, 1997
Let (1) \(\xi_1,\dots,\xi_n,\dots\) be a sequence of independent integer-valued random variables. Denote \(S_{n,k}= \xi_{k+1}+\cdots+ \xi_{k+n}\), \(A_{k,n}= ES_{k,n}\), \(B^2_{k,n}= DS_{k,n}\), \(S_{0,n}= S_n\), \(B^2_{0,n}= B^2_n\), \(A_{0,n}= A_n\). The sequence (1) is said to satisfy the local limit theorem if \[ P(S_n= m)= B^{-1}_n\exp\{(m- A_n)^2/
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A strong limit theorem in the Kac–Zwanzig model

Nonlinearity, 2008
A strong limit theorem is proved for a version of the well-known Kac–Zwanzig model, in which a 'distinguished' particle is coupled to a bath of N free particles through linear springs with random stiffness. It is shown that the evolution of the distinguished particle, albeit generated from a deterministic set of dynamical equations, converges pathwise ...
G Ariel, E Vanden-Eijnden
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Strong limit theorems: the strong law of large numbers

1995
Abstract The second part of this lemma was found by Erdös and Renyi. In a traditional formulation of the Borel-Cantelli lemma the condition of pairwise independence is replaced by the stronger condition of the mutual independence of the events A1, ... , An for every n.
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Majorizing potentials in strong ratio limit theorems

Mathematical Notes, 2008
In [1], the strong ratio limit theorems associated with Markov chains were first proved for some “test” functions with specific properties and were then generalized to a wider family of functions. In the present paper, this family is significantly extended by functions that can be majorized in a sense by the potentials of the original functions.
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