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1.
Precise asymptotics in the Baum-Katz and davis law of large numbers for positively associated sequences 总被引:6,自引:1,他引:5
§ 1 Introduction and resultsL et { X,Xi;i≥ 1} be a sequence of i.i.d.random variables,and set Sn= ni=1 Xi,n≥1.Hsu and Robbins[1 ] introduced the conceptof complete convergence.They together withErdos[2 ] proved n≥ 1 P(|Sn|≥εn) <∞ ,ε>0 (1)if and only if EX=0 and EX2 <∞ .L ater,Spitzer[3] proved n≥ 11n P(|Sn|≥εn) <∞ ,ε>0if and only if EX =0 and E|X|<∞ .More generally,it was shown by Baum and Katz[4 ]that,for 0
0 (… 相似文献
2.
§ 1 IntroductionIn[1 ] ,Karakostas and Tsamatos studied the existence of positive solutions for two-pointboundary value problemx″+ sign( 1 -c) q( t) f( x,x′) x′=0 ,( 1 .1 )x( 0 ) =0 ,x′( 1 ) =cx′( 0 ) ,( 1 .2 )where c∈ ( 0 ,1 )∪ ( 1 ,∞ ) .By using indices ofconvergence ofthe nonlinearity at0 and +∞and fixed point theorem in cones,they provided a priori upper and lower bounds for theslope of the solutions.The“c∈ ( 0 ,1 ) part”of their results has been extended to the fol-lowing … 相似文献
3.
The following assertion is proved. Let
be the set of integers the number of the prime power of which is
. Let
be the size of
. Then for each irrational
, uniformly in
, \begin{equation*} \frac{1}{\pi_k(x)} \bigg|\sum _{\alul{n\le x}{n\in\cN_k}} f(n) e^{2\pi in\alpha}\bigg|\to 0, \end{equation*}
where
is an arbitrary multiplicative function with
,
is a positive constant.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
4.
We define the reduced minimum modulus
of a nonzero element a in a unital C
*-algebra
by
. We prove that
. Applying this result to
and its closed two side ideal
, we get that dist
,
and
for any
if RR
= 0, where
and
is the quotient homomorphism and
. These results generalize corresponding results in Hilbert spaces. 相似文献
5.
Let
and
. We are interested in the lower bounds of the integral:
where h > 0 and
. Using the lower bounds for these integrals we obtain in particular for the so-called Fejér operator
of
the following asymptotic expression
which essentially improves the results concerning the approximation behavior of this operator.
Received: 10 January 2006 相似文献
6.
Dong Zhe 《Czechoslovak Mathematical Journal》2006,56(2):287-298
In this paper we investigate finite rank operators in the Jacobson radical
of Alg(
), where
are nests. Based on the concrete characterizations of rank one operators in Alg(
) and
, we obtain that each finite rank operator in
can be written as a finite sum of rank one operators in
and the weak closure of
equals Alg(
) if and only if at least one of
is continuous. 相似文献
7.
WUSHAOPING YANGHAITAO 《高校应用数学学报(英文版)》1998,13(3):251-262
Some existence and multiplicity of homoelinic orbits for second order Hamiltonian system x-a(t)x f(t,x)=0 are given by means of variational methods, where the function -1/2a(t)|s|^2∫^t0f(t,s)ds is asymptotically quadratic in s at infinity and subquadratic in s at zero, and the function a (t) mainly satisfies the growth condition limt→∞∫^t 1 t a(t)dt= ∞,VI∈R^1.A resonance case as well as a noncompact case is discussed too. 相似文献
8.
Let {X, X
n;n≥1} be a strictly stationary sequence of ρ-mixing random variables with mean zero and finite variance. Set
. Suppose lim
n→∞
and
, where d=2, if −1<b<0 and d>2(b+1), if b≥0. It is proved that, for any b>−1,
, where Γ(•) is a Gamma function.
Research supported by the National Natural Science Foundation of China (10071072). 相似文献
9.
V. D. Lyakhovsky 《Theoretical and Mathematical Physics》2006,148(1):968-979
In accordance with the quantum duality principle, the twisted algebra
is equivalent to the quantum group
and has two preferred bases: one inherited from the universal enveloping algebra
and the other generated by coordinate functions of the dual Lie group
. We show howthe transformation
can be explicitly obtained for any simple Lie algebra and a factorable chain
of extended Jordanian twists. In the algebra
, we introduce a natural vector grading
, compatible with the adjoint representation of the algebra. Passing to the dual-group coordinates allows essentially simplifying
the costructure of the deformed Hopf algebra
, considered as a quantum group
. The transformation
can be used to construct new solutions of the twist equations. We construct a parameterized family of extended Jordanian
deformations
and study it in terms of
; we find new realizations of the parabolic twist.
Dedicated to the birthday of my teacher, Yurii Novozhilov
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 148, No. 1, pp. 112–125, July, 2006. 相似文献
10.
We consider a Skorohod map
which takes paths in
to paths which stay in the positive orthant
. We let
be the domain of definition of
. A convex and lower semi-continuous function
and a set
are given. We are concerned with the calculation of the infimum of the value
for t ⩾ 0 and absolutely continuous
subject to the conditions
and
. We show that such minimization problems characterize large deviation asymptotics of tail probabilities of the steady-state
distribution of certain reflected processes. We approximate the infimum by a sequence of finite-dimensional minimization problems.
This approximation allows to formulate an algorithm for the calculation of the infimum and to derive analytical bounds for
its value. Several applications are discussed including large deviations of generalized processor sharing and large deviations
of heavily loaded queueing networks.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献