One-Sided Refinements of the Strong Law of Large Numbers and the Glivenko-Cantelli Theorem
نویسندگان
چکیده
منابع مشابه
A Note on the Strong Law of Large Numbers
Petrov (1996) proved the connection between general moment conditions and the applicability of the strong law of large numbers to a sequence of pairwise independent and identically distributed random variables. This note examines this connection to a sequence of pairwise negative quadrant dependent (NQD) and identically distributed random variables. As a consequence of the main theorem ...
متن کاملThe Glivenko Cantelli Theorem and its Generalizations
In this note we will study upper bounds of random variables of the type sup A∈A |ν n (A) − ν(A)| , where A is a class of sets that needs to fulll certain assumptions. These bounds are important tools in the analysis of learning processes and probabilistic theories of pattern recognition. The presentation given here is based on [DGL96].
متن کاملBorel-Cantelli lemmas and the law of large numbers
k=n Ak. If E occurs, then infinitely many of Ak:s occur. Sometimes we write this as E = {An i.o.} where i.o. is to be read as ”infinitely often”, i.e., infinitely many times. E is sometimes denoted with lim supAk. We need a couple of auxiliary results (the lemmas below) of probability calculus (found, e.g., on page 3 of [1]) that are basic in the sense that they are derived directly from the Ko...
متن کاملthe analysis of the role of the speech acts theory in translating and dubbing hollywood films
از محوری ترین اثراتی که یک فیلم سینمایی ایجاد می کند دیالوگ هایی است که هنرپیش گان فیلم میگویند. به زعم یک فیلم ساز, یک شیوه متأثر نمودن مخاطب از اثر منظوره نیروی گفتارهای گوینده, مثل نیروی عاطفی, ترس آور, غم انگیز, هیجان انگیز و غیره, است. این مطالعه به بررسی این مسأله مبادرت کرده است که آیا نیروی فراگفتاری هنرپیش گان به مثابه ی اعمال گفتاری در پنج فیلم هالیوودی در نسخه های دوبله شده باز تولید...
15 صفحه اولStrong Law of Large Numbers and Functional Central Limit Theorem
20.1. Additional technical results on weak convergence Given two metric spaces S1, S2 and a measurable function f : S1 → S2, suppose S1 is equipped with some probability measure P. This induces a probability measure on S2 which is denoted by Pf−1 and is defined by Pf−1(A) = P(f−1(A) for every measurable set A ⊂ S2. Then for any random variable X : S2 → R, its expectation EPf −1 [X] is equal to ...
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: 1992
ISSN: 0091-1798
DOI: 10.1214/aop/1176989688