Nonconventional large deviations theorems
نویسندگان
چکیده
منابع مشابه
Nonconventional Limit Theorems
The polynomial ergodic theorem (PET) which appeared in [1] and attracted substantial attention in ergodic theory studies the limits of expressions having the form 1/N ∑n=1 T q1(n) f1 · · ·T ql(n) fl where T is a weakly mixing measure preserving transformation, fi’s are bounded measurable functions and qi’s are polynomials taking on integer values on the integers. Motivated partially by this res...
متن کاملNonconventional Limit Theorems in Averaging
We consider ”nonconventional” averaging setup in the form dX(t) dt = ǫB ` X(t), ξ(q1(t)), ξ(q2(t)), ..., ξ(ql(t)) ́ where ξ(t), t ≥ 0 is either a stochastic process or a dynamical system (i.e. then ξ(t) = F x) with sufficiently fast mixing while qj(t) = αjt, α1 < α2 < ... < αk and qj , j = k+1, ..., l grow faster than linearly. We show that the properly normalized error term in the ”nonconventio...
متن کاملStone-Weierstrass type theorems for large deviations
We give a general version of Bryc’s theorem valid on any topological space and with any algebra A of real-valued continuous functions separating the points, or any wellseparating class. In absence of exponential tightness, and when the underlying space is locally compact regular and A constituted by functions vanishing at infinity, we give a sufficient condition on the functional Λ(·)|A to get ...
متن کاملLarge deviations of combinatorial distributions II: Local limit theorems
This paper is a sequel to our paper [17] where we derived a general central limit theorem for probabilities of large deviations1 applicable to many classes of combinatorial structures and arithmetic functions; we consider corresponding local limit theorems in this paper. More precisely, given a sequence of integral random variables {Ωn}n≥1 each of maximal span 1 (see below for definition), we a...
متن کاملLarge Deviations of Combinatorial Distributions I: Central Limit Theorems
We prove a general central limit theorem for probabilities of large deviations for sequences of random variables satisfying certain natural analytic conditions. This theorem has wide applications to combinatorial structures and to the distribution of additive arithmetical functions. The method of proof is an extension of Kubilius’ version of Cramér’s classical method based on analytic moment ge...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Probability Theory and Related Fields
سال: 2013
ISSN: 0178-8051,1432-2064
DOI: 10.1007/s00440-013-0481-4