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1.
For double arrays of constants {a
ni, 1≤i≤k
n, n≥1} and NA r.v. 's {X
n, n≥1}, conditions for almost sure convergence of
are given. Both casesk
n ↑ ∞ andk
n=∞ are treated. A Marcinkiewicz-type theorem for i. d. NA sequences is obtained as a special case.
Supported by the National Natural Science Foundation of China
Cheng Riyan: born in 1968, MS student 相似文献
2.
Gan Shixin 《武汉大学学报:自然科学英文版》1997,2(1):13-18
In this paper we prove the following Hàjek-Rènyi inequality: Let 0≤p≤1, then for any Banach spaceB, anyL
p integrableB valued random variable sequence {D
n
, n≥1}, any real number sequence {b
n
, n≥1} with 0<b
n, ↑ ∞, any integern≥1, there exist a constantC=C
p>0 (only depending onp) such that
In the other direction, we prove some strong laws of large numbers and the integrability of the maximal functions forB valued random variable sequences by using this inequality and the Hàjeck-Rènyi inequality we have obtained recently. Some
known results are extended and improved.
Supported by the National Natural Science Foundation of China and the State Education Commission PH. D Station Foundation
Gan Shixin: born in Feb. 1939, Professor 相似文献
3.
A branching model {Z n} n≥0is considered where the offspring distribution of the population's evolution is not only dependent on the population size, but also controlled by a Markovian environmental process {ξ n} n≥0. For this model, asymptotic behaviour is studied such as limn→∞Z n and limn→∞Z n/m n in the case that the mean m k, θof the offspring distribution converges to m>1 as the population size k grows to ∞. In the case that {ξ n} n≥0is an irreducible positive recurrent Markov chain, certain extinction (i.e. P(Z n=0 for some n)=1) and noncertain extinction (i.e. P(Z n=0 for some n)<1) are studied. 相似文献
4.
Gan Shi-xin 《武汉大学学报:自然科学英文版》2002,7(1):14-19
For weighted sums of the form
where {a
nj
, 1 ⩽j⩽k
n
↑∞,n⩾1} is a real constant array and {X
aj
, 1≤j≤k
n, n≥1} is a rowwise independent, zero mean, random element array in a real separable Banach space of typep, we establishL
r
convergence theorem and a general weak law of large numbers respectively, conversely, we characterize Banach spaces of typep in terms of convergence inr-th mean and probability for such weighted sums.
Foundation item: Supported by the National Natural Science Foundation of China (No. 10071058)
Biography: Gan Shi-xin (1939-), male, Professor, research direction: martingale theory, probability limiting theory and Banach
space geometry theory. 相似文献
5.
Let {(D
n, FFFn),n/->1} be a sequence of martingale differences and {a
ni, 1≤i≤n,n≥1} be an array of real constants. Almost sure convergence for the row sums
are discussed. We also discuss complete convergence for the moving average processes underB-valued martingale differences assumption.
Foundation item: Supported by the National Natural Science Foundation of China and the Doctoral Programme Foundation of China
Biography: DENG Ai-jiao (1974-), female, Ph.D. candidate. Research interest is in stochastic processes and random fractal. 相似文献
6.
DU Nailin School of Mathematics Statistics Wuhan University Wuhan Hubei China 《武汉大学学报:自然科学英文版》2006,11(3):486-492
0 IntroductionLeqtuiliHnebaer afo rHimlbaenrtd sap baoceun.dLeedtlianaenardfufnbceti oan baolu onndeHd ,serse--spectively. Our goal is to seekv∈Hsuchthata(u,v) =f(u) , u∈ H (1)As a rule, we call the expression (1) a variational equationandva solutiontothis equation.By virtue of the Riesz repre-sentationtheorem,there exists a uniquely determined boundedlinear operatorA:H→Hsuchthata(u,v) =〈u,Av〉, u,v∈ H,where〈·,·〉is the inner product onH.If the sesquilinearformais also with posit… 相似文献
7.
Peng Zhigang 《武汉大学学报:自然科学英文版》1997,2(2):139-141
We proved ifk(z)∈H
q (q≥1),g(z) is analytic on |z|=1,
, thenk′(z)∈H
1, especially, ifq=1, thenk(z) is an analytic function on the closed unit disk |z|≤1.
Peng Zhigang: born in June 1970, Ph. D 相似文献
8.
Let
(t)(t ∈ R
+
N
) be the d-dimensional N-parameter generalized Brownian sheet. We study the polar sets for
(t). It is proved that for any a ∈ R
d
, P{
(t) = a, for some t ∈ R
>
N
} =
and the probability that
(t) has k-multiple points is 1 or 0 according as whether 2kN > d(k − 1)β or 2kN < d(k−1)α. These results contain and extend the results of the Brownian sheet, where R
>
N
= (0,+∞)
N
,R
+
N
=[10,+∞)
N
,0< α≤1 and β≥1.
Biography: LI Huiqiong (1966–), female, Associate professor, research direction: stochastic process and random fractal. 相似文献
9.
Shixin Gan 《武汉大学学报:自然科学英文版》2009,14(1):6-10
In this paper some new results of strong stability of linear forms in φ-mixing random variables are given. It is mainly proved that for a sequence of φ-mixing random variables {x
n
, n ⩾ 1} and two sequences of positive numbers {a
n
, n ⩾ 1} and {b
n
, n ⩾ 1} there exist d
n
∈ R, n = 1,2,L, such that a.s. under some suitable conditions. The results extend and improve the corresponding theorems for independent identically
distributed random variables.
Foundation item: Supported by the National Natural Science Foundation of China(10671149) 相似文献
10.
In this paper,an exponential inequality for weighted sums of identically distributed NOD (negatively orthant dependent) random variables is established,by which we obtain the almost sure convergence rate of which reaches the available one for independent random variables in terms of Berstein type inequality. As application,we obtain the relevant exponential inequality for Priestley-Chao estimator of nonparametric regression estimate under NOD samples,from which the strong consistency rate is also obtained. 相似文献
11.
Hong Shaofang 《科学通报(英文版)》1998,43(4):275-275
Letm, n andk be positive integers, m> 1 andk≤ n. Let ‰
m
=‰m‰ denote the residue class ring modulom. Let ‰
m
denote the group of additive characters of ‰
m
denote the identity of ‰
m
. A necessary and sufficient condition for the systemf
1,...,f
k
∈ ‰
m
[x
1, ...,x
m
] to be orthogonal is given: for all additive characters ψ1, ..., ψ
k
∈ ‰
m
with ψi,≠x0 forsomei,
. As corollaries, the result of Shiue-Sun-Zhang and the result of Sun are obtained. 相似文献
12.
Let {Xn, n≥1} be a martingale difference sequence and {a
nk
, 1⩽k⩽n,n⩾1} an array of constant real numbers. The limiting behavior of weighted partial sums ∑
k=1
n
a
nk
X
k
is investigated and some new results are obtained.
Foundation item: Supported by the National Natural Sciene Foundation of China (No. 10071058 and No. 10071019)
Biography: Gan Shi-xin (1939-), male, Prof lessor, research direction: martingale theory, probability limiting theory and
Banach space geometry theory. 相似文献
13.
Some limit theorems for weighted sums of random variable fields 总被引:1,自引:0,他引:1
GAN Shixin~ CHEN Pingyan~ . School of Mathematics Statistics Wuhan University Wuhan Hubei China . Department of Mathematics Jinan University Guangzhou Guangdong China 《武汉大学学报:自然科学英文版》2006,11(2):323-327
1Preliminaries DuringthelastyearsthereappearedquiteafewpapersaboutlimittheoremsforBanachspacevaluedrandomvariables(r.v.’s)withmultidimensionalindex.Itistheaim ofthispapertogivecomparativeweakconditionswhichimply limittheoremsforweightedsumsofBanachspacevaluedr.v.fields.Thecurrentworkextendsthecorrespondingresultsof Refs.[15].Westartwithsomenotationsanddefinitions.LetNdbe thesetofalld dimensionallatticeofpointswithpositiveinte gersascomponents,whered≥1isafixedinteger.LetNdbe equippedwithco… 相似文献
14.
MING Ruixing MODIBO Diarra HU Yijun 《武汉大学学报:自然科学英文版》2007,12(3):407-411
Let R(t)=u+ct-∑ I=1^N(t) Xi,t≥0 be the renewal risk model, with Fx(x)being the distribution function of the claim amount X. Let ψ(u) be the ruin probability with initial surplus u. Under the condition of Fx(x) ∈ S^*(γ),y ≥ 0, by the geometric sum method, we derive the local asymptotic behavior for ψ(u,u + z] for every 0 ( z ( oo, On one hand, the asymptotic behavior of ψ(u) can be derived from the result obtained. On the other hand, the result of this paper can be applied to the insurance risk management of an insurance company. 相似文献
15.
It is well known that, the singular integral operatorS defined as:
ifL is a closed smooth contour in the complex plane C, thenS is a bounded linear operator fromH
μ(L) intoH
μ(L): ifL is an open smooth curve, thenS is just a linear operator fromH
* intoH
*. In this paper, we define a Banach space
, and prove that
is a bounded linear operator, then verify the boundedness of other kinds of singular integral operators.
Supported by the National Science Foundation of China
Wang Xiaolin: born in Aug. 1950, Professor 相似文献
16.
Zhong Li 《科学通报(英文版)》1997,42(24):2025-2025
The boundary value problem for harmonic maps of the Poincare disc is discussed. The emphasis is on the non-smoothness of the given boundary values in the problem. Let T . be a subspace of the universal Teichmüller space, defined as a set of normalized quasisymmetric homeomorphisms h of the unit circle S onto itself where h admits a quasiconformal extension to the unit disc D with a complex dilatation μ satisfying
where ρ(z)|dz|2 is the Poincare metric of D. Let B . be a Banach space consisting of holomorphic quadratic differentials φ in D with norms
It is shown that for any given quasisymmetric homeomorphism h : S1→S1∈ T . , there is a unique quasiconformal harmonic map of D with respect to the Poincare metric whose boundary corresponding is h and the Hopf differential of such a harmonic map belongs to B . 相似文献
17.
LetX be a complex quasi-Banach space and Φ:[0,∞)→[0,∞) an increasing convex function with Φ(0)=0,
and Φ∈Δ2. ThenL
Φ
*
(X) is a quasi-Banach space with continuous quasi-norm andL
Φ
*
(X) has the ARNP if and only ifX does.
Supported by the National Natural Science Foundation of China
Liu Peide: born in 1943, Professor 相似文献
18.
Che Ka-jia Li Zhi-chen College of Management Huazhong University of Science Technology Wuhan Hubei China 《武汉大学学报:自然科学英文版》2004,9(2):149-152
0 IntroductionIntheprocessofR&Ditem ,thereisusuallycompetition .ManyfirmswanttoinvestR&Dtoobtainapatent.Lury[1 ] gaveanequilibriuminvestmentundertheconditionofone timeinvestmentandcontinuousinvestmentwhenthepayoffwasafixedprize.Ref.[2 ]analyzedtheeffectofinformationsharinginR&D .TherearemanyliteraturesaboutanalysisofR&DlevelswhenfirmscompeteinoutputmarketafterR&Dsucceeds[3 ,4] .Additionally ,todecideinvestmentlevel,therearemanyliteraturesaboutR&Ditem’spricing .MondherBellalah[5] ,K .… 相似文献
19.
Pulsed laser photolysis/laser-induced fluorescence (LP-LIF) is utilized to measure rate constants for C2(a3Πu) reactions with NO, N2O, O2, H2 and NH3. Multiphoton dissociation of C2Cl4 at 266 nm is employed for the generation of C2(a3Πu) radicals. The C2(a3Πu) concentration is monitored by the fluorescence of the (0, 0) band of the (d3Πg8596;a3Πu) transition at 516.5 nm. C2(a3Πu) removal rate constants for the reactions are determined as kNO = (5.46 ± 0.10) × 10-11 cm3 molecule-1 s-1 , kN2O = (1.63 ± 0.20) × 10-13 cm3 molecule-1 s-1 , kN2O = (1.58 ± 0.16) × 10-11 cm3 molecule-1 s-1, kO2 = (5.92 ± 1.00) × 10-14 cm3 molecule-1 s-1, kH2< 1.0× 10-14 cm3 molecule-1 s-1. Based on the data analysis and theoretical calculation, we suggest that the C2(a3Πu) reactions with H2 and NH3 proceed via the hydrogen abstraction mechanism, barriers exist at the entrance channel of the reactions of C2(a3Πu) with H2 and NH3. 相似文献
20.
WEIXiao HUYi-jun 《武汉大学学报:自然科学英文版》2004,9(6):863-866
Consider an insurance risk model, in which the surplus process satisfies a recursive equation Un=Un-1(1 rn)-Xn for n≥1, where U0=x≥0 is the initial surplus, {rn;n≥1} the interest rate sequence, {Xn;n≥l} the sequence of i. i. d. real-valued random variables with common distribution function F, which denotes the gross loss during the nth year. We investigate the ruin probability within a finite time horizon and give the asymptotic result as x→∞. 相似文献