منابع مشابه
A Multidimensional Central Sets Theorem
t∈α xt : α ∈ Pf (ω)}. A set A ⊆ N is called an IP-set iff there exists a sequence 〈xn〉n=0 in N such that FS(〈xn〉n=0) ⊆ A. (This definitions make perfect sense in any semigroup (S, ·) and we indeed plan to use them in this context. FS is an abbriviation of finite sums and will be replaced by FP if we use multiplicative notation for the semigroup operation.) Now Hindman’s Theorem states that in a...
متن کاملA Multidimensional Central Sets Theorem
t∈α xt : α ∈ Pf (ω)}. A set A ⊆ N is called an IP-set iff there exists a sequence 〈xn〉n=0 in N such that FS(〈xn〉n=0) ⊆ A. (This definitions make perfect sense in any semigroup (S, ·) and we indeed plan to use them in this context. FS is an abbriviation of finite sums and will be replaced by FP if we use multiplicative notation for the semigroup operation.) Now Hindman’s Theorem states that in a...
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We consider the class of graph-directed constructions which are connected and have the property of finite ramification. By assuming the existence of a fixed point for a certain renormalization map, it is possible to construct a Laplace operator on fractals in this class via their Dirichlet forms. Our main aim is to consider the eigenvalues of the Laplace operator and provide a formula for the s...
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We study subgeometric convergence rates in the local renewal theorem, which plays an important role in obtaining results on convergence rates for Markov chains [4]. Let {ξn}n≥0 and {ξ ′ n}n≥0 be two sequences of mutually independent and integervalued r.v.’s. Assume further that (i) ξ0 and ξ ′ 0 are non-negative r.v.’s; (ii) all {ξn}n≥1 and {ξ ′ n}n≥1 are i.i.d. and strictly positive, with a com...
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provided Eξ1 is finite and positive (see, for example, Feller and Orey [8], Feller [7, Ch. XI], Woodroofe [25, Appendix]); F is called lattice if it is concentrated on some lattice {ka, k ∈ Z} with a > 0. If F is lattice the same is true when h is a multiple of the span a. It is proved in Wang and Woodroofe [23] and in Borovkov and Foss [5, Theorem 2.6] that (1) holds uniformly over certain cla...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 1976
ISSN: 0091-1798
DOI: 10.1214/aop/1176996034