Sums of independent random variables and the Burkholder transforms
نویسندگان
چکیده
منابع مشابه
Estimating Sums of Independent Random Variables
The paper deals with a problem proposed by Uriel Feige in 2005: if X1, . . . , Xn is a set of independent nonnegative random variables with expectations equal to 1, is it true that P ( ∑n i=1 Xi < n + 1) > 1 e ? He proved that P ( ∑n i=1Xi < n + 1) > 1 13 . In this paper we prove that infimum of the P ( ∑n i=1Xi < n + 1) can be achieved when all random variables have only two possible values, a...
متن کاملOn the Number of Positive Sums of Independent Random Variables
2 . The invariance principle . We first prove the following : If the theorem can be established for one particular sequence of independent random variables Y1, Y2, . . . satisfying the conditions of the theorem then the conclusion of the theorem holds for all sequences of independent random variables which satisfy the conditions of the theorem . In other words, if the limiting distribution exis...
متن کاملOn the Lower Limit of Sums of Independent Random Variables
1. Let X1 , X2 , • • • , Xn . . . be independent random variables and let Sn = X, . In the so-called law of the iterated logarithm, completely solved by Feller recently, the upper limit of S n as n -4 co is considered and its true order of magnitude is found with probability one . A counterpart to that problem is to consider the lower limit of Sn as n --> oo and to make a statement about its or...
متن کاملOn the Equidistribution of Sums of Independent Random Variables
where the constant M (A) is the mean value of A(x) as defined in the theory of almost periodic functions. Let it) —feitxdFix) denote the characteristic function of the X's. Concerning the roots of the equation o5(¿) = 1 one of the three following cases must hold. Case 1 ("General" case), (pit) = 1 if and only if t = 0. Case 2 ("Lattice" case). <p(f) is not identically equal to 1 but there ex...
متن کاملMeasuring the magnitude of sums of independent random variables
This paper considers how to measure the magnitude of the sum of independent random variables in several ways. We give a formula for the tail distribution for sequences that satisfy the so called Lévy property. We then give a connection between the tail distribution and the pth moment, and between the pth moment and the rearrangement invariant norms.
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: Proceedings of the American Mathematical Society
سال: 1977
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1977-0451392-6