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Lacunary Series and Strong Approximation. [PDF]
Entropy (Basel)Strong approximation, introduced by Strassen (1964), is one of the most powerful methods to prove limit theorems in probability and statistics. In this paper we use strong approximation of lacunary series with conditionally independent sequences to prove
Berkes I.
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Some strong limit theorems for nonhomogeneous Markov chains indexed by controlled trees [PDF]
Journal of Inequalities and Applications, 2016 In this paper, a kind of infinite, local finite tree T, named a controlled tree, is introduced. Some strong limit properties, such as the strong law of large numbers and the asymptotic equipartition property, for nonhomogeneous Markov chains indexed by T,
Weicai Peng +4 more
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Strong Limit Theorems for Dependent Random Variables
International Journal of Mathematical Models and Methods in Applied Sciences, 2021 In this article We establish moment inequality of dependent random variables, furthermore some theorems of strong law of large numbers and complete convergence for sequences of dependent random variables. In particular, independent and identically distributed Marcinkiewicz Law of large numbers are generalized to the case of m₀ -dependent sequences.
Libin Wu, LI Bai-nian
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Some Strong Limit Theorems in Averaging [PDF]
Communications in Mathematical PhysicsAbstractThe paper deals with the fast-slow motions setups in the discrete time $$X^{\varepsilon }((n+1){\varepsilon })=X^{\varepsilon }(n{\varepsilon })+{\varepsilon }B(X^{\varepsilon }(n{\varepsilon }),\xi (n))$$ X ε
Yuri Kifer
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Strong renewal theorem and local limit theorem in the absence of regular\n variation [PDF]
Journal of Theoretical Probability, 2020 32 pages, revised ...
Péter Kevei, Dalia Terhesiu
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Generalized Adiabatic Theorem and Strong-Coupling Limits [PDF]
Quantum, 2019 We generalize Kato's adiabatic theorem to nonunitary dynamics with an isospectral generator. This enables us to unify two strong-coupling limits: one driven by fast oscillations under a Hamiltonian, and the other driven by strong damping under a Lindbladian. We discuss the case where both mechanisms are present and provide nonperturbative error bounds.
Daniel Burgarth +4 more
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Strong ratio limit theorems associated with random walks [PDF]
, 2015 Strong ratio limit theorems associated with a broad class of spread out random walks on unimodular groups were proved in the preceding paper, where these random walks were assumed to have the convergence parameter $R=1$. In the present paper, we study the case of an arbitrary $R\ge1$ and clarify the role of the condition that the group is unimodular.
M. G. Shur
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Crossing bridges with strong Szegő limit theorem [PDF]
Journal of High Energy Physics, 2021 Abstract We develop a new technique for computing a class of four-point correlation functions of heavy half-BPS operators in planar $$ \mathcal{N} $$ N = 4 SYM theory which admit factorization into a product of two octagon form factors with an arbitrary bridge length.
Belitsky, A.V., Korchemsky, G.P.
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One bound to rule them all: from Adiabatic to Zeno [PDF]
Quantum, 2022 We derive a universal nonperturbative bound on the distance between unitary evolutions generated by time-dependent Hamiltonians in terms of the difference of their integral actions.
Daniel Burgarth +3 more
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Small deviation properties concerning arrays of non-homogeneous Markov information sources
Frontiers in Physics, 2023 In this study, we first define the logarithmic likelihood ratio as a measure between arbitrary generalized information sources and non-homogeneous Markov sources and then establish a class of generalized information sources for small deviation theorems ...
Ximei Qin +4 more
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