共查询到20条相似文献,搜索用时 125 毫秒
1.
Let {W(t) ,0≤t<∞ }beastandard ,one dimensionalBrownianmotionon (Ω ,F ,P) .Itiswellknownthat -∞ =liminft→∞ W(t) <limsupt→∞ W(t) =∞andaccordingtoKahance ([1 ] ,Theorem1 ,Chapter 1 2 ) ,ifasequence {tn,n≥ 1 )satisfies∑∞n=11tn<∞ ,thenlimn→∞ W(tn) =∞a .s.Wecallthesequence {W (tn) ,n≥ 1 }atransient… 相似文献
2.
本文利用初等方法证明∑∞n =11n4 =π490 .1 几个引理引理 1 ∑∞n =1cot2 nπ2m+1 =13 m(2m-1 ) ,∑mn ,l =1n<lcot2 nπ2m +1 cot2 lπ2m +1=13 0 m (m -1 ) (2m -2 ) (2m-3 ) .其中m、l、n等均表示整数 ,下同 .证明 由de·Movre公式得cos(2m +1 )α+isin(2m +1 )α=(cosα+isinα) 2m+1于是 ,cos(2m +1 )α+isin(2m+1 )α=∑mk =0(-1 ) kC2k2m+1cos2 (m-k) +1αsin2kα+i∑mk =0(-1 ) kC2k+12m+1cos2 (m-k) αsin2k+1α. (1 )比… 相似文献
3.
Letωbethespaceofallscalarvaluedsequences,and φitssubspacewithonlyfinitelymanynon zerocoordinates.AlinearsubspaceEofωiscalledasequencespace. Wesaythatanon zerovectorsequence {z(n) }inωisablocksequenceifthereexistsastrictlyincreasingsequenceofpositiveinteger… 相似文献
4.
§1. IntroductionIn1967,Teicherprovedthat[1]E(Supn|Sn|nL2n)p<+∞, iffEX2log+|X|L2|X|<+∞,p=2E|X|p<+∞,p>2 . Where{X,Xn,n≥1}isasequenceofi.i.drealrandomvariableswithmeanszero.In1995,Thesimilarresultshavebeensetupfori.i.drandomvariables{X,Xnn≥1}withmean… 相似文献
5.
§ 1.Introduction LetBnbetheunitballinCn,anddvthenormalizedLebesguemeasureonBn.SobolevspaceL2 ,1isthespaceoffunctionsu :Bn→C ,forwhichthenorm‖u‖1/ 2 =∑ni=1 ∫Bn u zi(z) 2 + u zi(z) 2 dν1/ 2 <∞ .L2 ,1/ 2 isaHilbertspacewiththeinnerproduct〈u ,v〉1/ 2 =∑ni=1〈 u zi, u zi〉L2 (dν) +∑ni=1〈 u zi, u … 相似文献
6.
1 IntroductionInthispaper,weconsiderthefollowingperiodicinitialvalueproblemforthesystemofGinzburg LandauequationscoupledwithBBMequations:x∈Rεt+ με-(α1+iα2 )εxx+ (β1+iβ2 ) |ε|2 ε-iδnε=g1(x) ,(1 .1 )nt+ f(n) x+λn-αnxx-nxxt+ |ε|2 x =g2 (x) ,(1 .2 )ε(x+ 2π ,t) =ε(x ,t) ,n(x + 2π ,t) =n(x ,t) ,(1 .3)ε(x ,0 )… 相似文献
7.
1 IntroductionForsolvingstiffinitialvalueproblemsforsystemsofODEsy′=f(y) ,y(t0 ) =y0 ,t0 <t≤T ,y0 ,y∈Rm,f :Ω Rm →Rm (1 .1 )manyparticularone blockmethodsoftheformYn+1= AYn+h( B0 F(Yn) + B1F(Yn+1) ) , A =A Im, Bi=Bi Im,A ,Bi∈Rr×r,Yn =(YTnr,… ,yT(n+1)r- 1) T,F(Yn) =(fT(ynr) ,… ,fT(y(n+1)r- 1) ) T,yj≈ y(tj) ,… 相似文献
8.
命题 设n (n≥ 2 )为自然数 ,则 sinnx =∑0≤j≤ m2C2j 1n ( - 1 ) j ·sin2j 1xcosn -2j-1x ( 1 ) cosnx =∑0≤j≤ m2C2 jn( - 1 ) jsin2 jxcosn -2 jx( 2 ) tgnx =∑0≤j≤ m2( - 1 ) jC2j 1n tg2j 1x∑0≤j≤ m2C2 jn( - 1 ) jtg2 jx ( 3)证 cosnx isinnx =(icosx sinx) n =∑0≤k≤m Ckniksinkxcosn -kx =∑0≤j≤ m2C2jn( - 1 ) jsin2jxcosn -2jx (∑0≤j≤ m2C2j 1n ( - 1… 相似文献
9.
§1.IntroductionConsiderthemodelgivenbyYi=xiτβ g(ti) εi,i=1,…,(1.1)wherexi=(xi1,…,xip)τ(p1)andti(ti∈[0,1])areknowndesignpoints,β=(β1,…,βp)τisanunknownparametervectorandgisanunknownfunction,andεiarei.i.d.randomerrorswithzero0andvarianceσ2.Themodeldefinedin(1.1)belongstotheclass… 相似文献
10.
张吉慧 《高校应用数学学报(英文版)》2003,18(1):45-52
§ 1 IntroductionWeconsiderthefourthordersemilinearsubellipticboundaryvalueproblemΔ2 Hu +cΔHu =f( (z ,t) ,u) inD ,u|D =ΔHu|D =0 ,( 1 .1 )whereDisaboundedopensubsetoftheHeisenberggroupHnandΔHisthesubellipticLapla cianonHn.WerecallthatHnistheLiegroupwhoseunderlyingmani… 相似文献
11.
De Li LI Fu Xing ZHANG Andrew ROSALSKY 《数学学报(英文版)》2007,23(3):557-562
Let {X, Xn; n≥ 1} be a sequence of i.i.d. Banach space valued random variables and let {an; n ≥ 1} be a sequence of positive constants such that
an↑∞ and 1〈 lim inf n→∞ a2n/an≤lim sup n→∞ a2n/an〈∞
Set Sn=∑i=1^n Xi,n≥1.In this paper we prove that
∑n≥1 1/n P(||Sn||≥εan)〈∞ for all ε〉0
if and only if
lim n→∞ Sn/an=0 a.s.
This result generalizes the Baum-Katz-Spitzer complete convergence theorem. Combining our result and a corollary of Einmahl and Li, we solve a conjecture posed by Gut. 相似文献
12.
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
13.
Wang Lei Pan Ting Dept. of Math. Zhejiang Univ. Hangzhou China. Univ. of International Relation Hangzhou China. 《高校应用数学学报(英文版)》2004,19(2):212-222
Ibαf ( x) =∫R ∏mj=1( bj( x) - bj( y) ) 1| x - y| n-αf ( y) dyare considered.The following priori estimates are proved.For 1
01Φ1t| {y∈Rn:| Ibαf( y) | >t}| 1q ≤csupt>01Φ1t| {y∈Rn:ML( log L) 1r ,α(‖b‖f ) ( y) >t}| 1q,where‖b‖=∏mj=1‖bj‖Oscexp Lrj,Φ( t) =t( 1 + log+t) 1r,1r =1r1+ ...+ 1rm,ML(… 相似文献
14.
De Li LI Andrew ROSALSKY Andrei VOLODIN 《数学学报(英文版)》2007,23(4):599-612
For a sequence of i.i.d. Banach space-valued random variables {Xn; n ≥ 1} and a sequence of positive constants {an; n ≥ 1}, the relationship between the Baum-Katz-Spitzer complete convergence theorem and the law of the iterated logarithm is investigated. Sets of conditions are provided under which
(i) lim sup n→∞ ||Sn||/an〈∞ a.s.and
∞ ∑n=1(1/n)P(||Sn||/an ≥ε〈∞for all ε 〉 λ for some constant λ ∈ [0, ∞) are equivalent;
(ii) For all constants λ ∈ [0, ∞),
lim sup ||Sn||/an =λ a.s.and ^∞∑ n=1(1/n) P(||Sn||/an ≥ε){〈∞, if ε〉λ =∞,if ε〈λare equivalent. In general, no geometric conditions are imposed on the underlying Banach space. Corollaries are presented and new results are obtained even in the case of real-valued random variables. 相似文献
15.
Oscillation for systems of nonlinear neutral type parabolic partial functional differential equations 总被引:14,自引:0,他引:14
YANGJUN GUANXINPING 《高校应用数学学报(英文版)》1997,12(2):165-178
This paper discusses the oscillation of solutions for systems of nonlinear neutral type parabolic partial fuctional differential equations of the form 相似文献
16.
García-Caballero Esther M. Moreno Samuel G. Marcellán Francisco 《Periodica Mathematica Hungarica》2003,46(2):157-170
In this contribution we analyze the generating functions for polynomials orthogonal with respect to a symmetric linear functional
u, i.e., a linear application in the linear space of polynomials with complex coefficients such that
. In some cases we can deduce explicitly the expression for the generating function
where {Pn}n is the sequence of orthogonal polynomials with respect to u.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
17.
Using the following notation: C is the space of continuous bounded functions f equipped with the norm
, V is the set of functions f such that
, the set E consists of fCV and possesses the following property:
is summable on each finite interval,
we establish some assertions similar to the following theorem: Let
0$$
" align="middle" border="0">
,
Then for fV the series
uniformly converges with respect to
and the following equality holds:
This theorem develops some results obtained by Zubov relative to the approximation of probability distributions. Bibliography: 4 titles. 相似文献
18.
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
19.
We prove that there exists a series of the form (*)
, where {nk(x)} is a subsystem of either the trigonometric or the Walsh system such that
; where n as n and for each > 0 a weight function (x) can be constructed such that 0 < (x) 1,
, and series (*) is universal in the space L1
with respect simultaneously to rearrangements as well as to subseries. 相似文献
20.
Precise Asymptotics in the Law of the Iterated Logarithm of Moving-Average Processes 总被引:1,自引:0,他引:1
Yun Xia LI Li Xin ZHANG 《数学学报(英文版)》2006,22(1):143-156
In this paper, we discuss the moving-average process Xk = ∑i=-∞ ^∞ ai+kεi, where {εi;-∞ 〈 i 〈 ∞} is a doubly infinite sequence of identically distributed ψ-mixing or negatively associated random variables with mean zeros and finite variances, {ai;-∞ 〈 i 〈 -∞) is an absolutely solutely summable sequence of real numbers. 相似文献