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Strong limit theorems for anisotropic random walks on ℤ2
Periodica Mathematica Hungarica, 2013We 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 +3 more
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On Strong Limit Theorems for Sums of Independent Random Variables
Theory of Probability & Its Applications, 1993zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Martikaĭnen, A. I., Petrov, V. V.
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Uniform Integrability for Strong Ratio Limit Theorems. I
Theory of Probability & Its Applications, 2006Unlike 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, 1997Let (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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Strong limit theorems: the strong law of large numbers
1995Abstract 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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A strong limit theorem in the Kac–Zwanzig model
Nonlinearity, 2008A 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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Free versions of the strong Szegő limit theorem
The Strong Szegő Limit Theorem is a theorem about the asymptotics of the determinants of large Toeplitz matrices. It can be reformulated as a probabilistic statement about eigenvalue statistics of random unitary matrices. We prove a multivariate generalization of the theorem in this latter form, replacing a single unitary with a system of independent ...Jury, Michael T. +2 more
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Strong Limit Theorems for Increments of Random Fields
2012After reconsidering the oscillating behaviour of sums of i.i.d. random variables we study the oscillating behavior for sums over i.i.d. random fields under exact moment conditions. This summarizes several papers published jointly with A. Gut (Uppsala).
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Strong limit theorems: the law of the iterated logarithm
1995Abstract Theorem 7.1 is in some sense as sharp as possible. Namely, if we replace o by O in the condition (7.1), the assertion of the theorem may fail. Using the arguments that we employed in the proof of Theorem 7.1, we can prove the following proposition on the connection between an estimate of the remainder term in the central limit ...
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A Strong Limit Theorem for Random Sets
Advances in Applied Probability, 1978openaire +1 more source