Almost Sure Invariance Principles for Partial Sums of Mixing $B$-Valued Random Variables
نویسندگان
چکیده
منابع مشابه
The Almost Sure Convergence for Weighted Sums of Linear Negatively Dependent Random Variables
In this paper, we generalize a theorem of Shao [12] by assuming that is a sequence of linear negatively dependent random variables. Also, we extend some theorems of Chao [6] and Thrum [14]. It is shown by an elementary method that for linear negatively dependent identically random variables with finite -th absolute moment the weighted sums converge to zero as where and is an array of...
متن کاملTHE ALMOST SURE CONVERGENCE OF WEIGHTED SUMS OF NEGATIVELY DEPENDENT RANDOM VARIABLES
In this paper we study the almost universal convergence of weighted sums for sequence {x ,n } of negatively dependent (ND) uniformly bounded random variables, where a, k21 is an may of nonnegative real numbers such that 0(k ) for every ?> 0 and E|x | F | =0 , F = ?(X ,…, X ) for every n>l.
متن کاملAlmost sure convergence of weighted sums of independent random variables
Let (Ω,F ,P) be a probability space, and let {Xn} be a sequence of integrable centered i.i.d. random variables. In this paper we consider what conditions should be imposed on a complex sequence {bn} with |bn| → ∞, in order to obtain a.s. convergence of P n Xn bn , whenever X1 is in a certain class of integrability. In particular, our condition allows us to generalize the rate obtained by Marcin...
متن کاملOn the Interrelation of Almost Sure Invariance Principles for Certain Stochastic Adaptive Algorithms and for Partial Sums of Random Variables I
where {xi, i = 1, 2, 3,..} is a sequence of random vectors and {Xt, t>_.0} is a Brownian motion. In this note, we show that if {Ak, k = 1, 2, 3,...} and {bk, k--1, 2, 3,...} are processes satisfying almost-sure bounds analogous to Eq. (1), (where { X , t />0} could be a more general Gauss -Markov process) then {hk, k = I, 2, 3,...}, the solution of the stochastic approximation or adaptive filte...
متن کاملAlmost Sure Stability of Partial Sums of Uniformly Bounded Random Variables
Suppose al, a2,... is a sequence of real numbers with a,, oo. If lim sup( Xl + + X, )/a,, = a a.s. for every sequence of independent nonnegative uniformly bounded random variables Xi, X2,... satisfying some hypothesis condition A, then for every (arbitrarily-dependent) sequence of nonnegative uniformly bounded random variables Y1, Y2,..., lim sup( Y, + + Y, )/a,, = a a.s. on the set where the c...
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: 1980
ISSN: 0091-1798
DOI: 10.1214/aop/1176994565