The Central Limit Theorem and Poincare-Type Inequalities
نویسندگان
چکیده
منابع مشابه
Entropy inequalities and the Central Limit Theorem
Motivated by Barron (1986, Ann. Probab. 14, 336–342), Brown (1982, Statistics and Probability: Essays in Honour of C.R. Rao, pp. 141–148) and Carlen and So er (1991, Comm. Math. Phys. 140, 339–371), we prove a version of the Lindeberg–Feller Theorem, showing normal convergence of the normalised sum of independent, not necessarily identically distributed random variables, under standard conditio...
متن کاملCentral Limit Theorem in Multitype Branching Random Walk
A discrete time multitype (p-type) branching random walk on the real line R is considered. The positions of the j-type individuals in the n-th generation form a point process. The asymptotic behavior of these point processes, when the generation size tends to infinity, is studied. The central limit theorem is proved.
متن کاملPoincare Inequalities
Poincare inequalities are a simple way to obtain lower bounds on the distortion of mappings X into Y. These are shown below to be sharp when we consider the Lp spaces. A Poincare inequality is one of the following type: suppose Ψ : [0, ∞) → [0, ∞) is a nondecreasing function and that au,v, bu,v are finite arrays of real numbers (for u, v ∈ X, and not all of the numbers 0). We say that functions...
متن کاملThe Martingale Central Limit Theorem
One of the most useful generalizations of the central limit theorem is the martingale central limit theorem of Paul Lévy. Lévy was in part inspired by Lindeberg’s treatment of the central limit theorem for sums of independent – but not necessarily identically distributed – random variables. Lindeberg formulated what, in retrospect, is the right hypothesis, now known as the Lindeberg condition,1...
متن کاملThe Lindeberg central limit theorem
Theorem 1. If μ ∈P(R) has finite kth moment, k ≥ 0, then, writing φ = μ̃: 1. φ ∈ C(R). 2. φ(v) = (i) ∫ R x edμ(x). 3. φ is uniformly continuous. 4. |φ(v)| ≤ ∫ R |x| dμ(x). 1Charalambos D. Aliprantis and Kim C. Border, Infinite Dimensional Analysis: A Hitchhiker’s Guide, third ed., p. 515, Theorem 15.15; http://individual.utoronto.ca/ jordanbell/notes/narrow.pdf 2Onno van Gaans, Probability measu...
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: The Annals of Probability
سال: 1988
ISSN: 0091-1798
DOI: 10.1214/aop/1176991902