共查询到20条相似文献,搜索用时 31 毫秒
1.
It is shown that if {y
n} is a block of type I of a symmetric basis {x
n} in a Banach spaceX, then {y
n} is equivalent to {x
n} if and only if the closed linear span [y
n] of {y
n} is complemented inX. The result is used to study the symmetric basic sequences of the dual space of a Lorentz sequence spaced(a, p). Let {x
n,f
n} be the unit vector basis ofd(a, p), for 1≤p<+∞. It is shown that every infinite-dimensional subspace ofd(a, p) (respectively, [f
n] has a complemented subspace isomorphic tol
p (respectively,l
q, 1/p+1/q=1 when 1<p<+∞ andc
0 whenp=1) and numerous other results on complemented subspaces ofd(a, p) and [f
n] are obtained. We also obtain necessary and sufficient conditions such that [f
n] have exactly two non-equivalent symmetric basic sequences. Finally, we exhibit a Banach spaceX with symmetric basis {x
n} such that every symmetric block basic sequence of {x
n} spans a complemented subspace inX butX is not isomorphic to eitherc
0 orl
p, 1≤p<+∞. 相似文献
2.
Z. Altshuler 《Israel Journal of Mathematics》1976,24(1):39-44
A Banach spaceX with symmetric basis {e
n} is isomorphic toc
0 orl
p for some 1≦p<∞, if all symmetric basic sequences inX are equivalent to {e
n}, and all symmetric basic sequences in [f
n]≠X
* are equivalent to {f
n} (wheref
n
(e
j
) =δ
n, j
). The result proved in the paper is actually stronger, in the sense that it does not involve all symmetric basic sequences,
but only the so called sequences generated by one vector.
This is part of the author’s Ph.D. Thesis prepared at the Hebrew University of Jerusalem under the supervision of Professor
L. Tzafriri. I wish to thank Professor Tzafriri for his interest and advice. 相似文献
3.
StrongwayShi 《高校应用数学学报(英文版)》2000,15(1):45-54
Abstract. Let {Xn,n≥1} be a stationary strongly mixing random sequence satisfying EX1=u, 相似文献
4.
For each n≥1, let {X j,n }1≤j≤n be a sequence of strictly stationary random variables. In this article, we give some asymptotic weak dependence conditions for the convergence in distribution of the point process $N_{n}=\sum_{j=1}^{n}\delta_{X_{j,n}}For each n≥1, let {X
j,n
}1≤j≤n
be a sequence of strictly stationary random variables. In this article, we give some asymptotic weak dependence conditions
for the convergence in distribution of the point process
Nn=?j=1ndXj,nN_{n}=\sum_{j=1}^{n}\delta_{X_{j,n}}
to an infinitely divisible point process. From the point process convergence we obtain the convergence in distribution of
the partial sum sequence S
n
=∑
j=1
n
X
j,n
to an infinitely divisible random variable whose Lévy measure is related to the canonical measure of the limiting point process.
As examples, we discuss the case of triangular arrays which possess known (row-wise) dependence structures, like the strong
mixing property, the association, or the dependence structure of a stochastic volatility model. 相似文献
5.
6.
Let {X
n}
n
=1/∞
be a sequence of random variables with partial sumsS
n, and let {ie241-1} be the σ-algebra generated byX
1,…,X
n. Letf be a function fromR toR and suppose {ie241-2}. Under conditions off and moment conditions on theX'
ns, we show thatS
n/n converges a.e. (almost everywhere). We give several applications of this result.
Research supported by N.S.F. Grant MCS 77-26809 相似文献
7.
Let Φ be a symmetric function, nondecreasing on [0,∞) and satisfying a Δ2 growth condition, (X
1,Y
1), (X
2,Y
2),…,(X
n
,Y
n
) be arbitrary independent random vectors such that for any given i either Y
i
=X
i
or Y
i
is independent of all the other variates. The purpose of this paper is to develop an approximation of
valid for any constants {a
ij
}1≤
i,j≤n
, {b
i
}
i
=1
n
, {c
j
}
j
=1
n
and d. Our approach relies primarily on a chain of successive extensions of Khintchin's inequality for decoupled random variables
and the result of Klass and Nowicki (1997) for non-negative bilinear forms of non-negative random variables. The decoupling
is achieved by a slight modification of a theorem of de la Pe?a and Montgomery–Smith (1995).
Received: 25 March 1997 / Revised version: 5 December 1997 相似文献
8.
A. I. Martikainen 《Journal of Mathematical Sciences》2006,133(3):1308-1313
Let {Xi, Yi}i=1,2,... be an i.i.d. sequence of bivariate random vectors with P(Y1 = y) = 0 for all y. Put Mn(j) = max0≤k≤n-j (Xk+1 + ... Xk+j)Ik,j, where Ik,k+j = I{Yk+1 < ⋯ < Yk+j} denotes the indicator function for the event in brackets, 1 ≤ j ≤ n. Let Ln be the largest index l ≤ n for which Ik,k+l = 1 for some k = 0, 1, ..., n - l. The strong law of large numbers for “the maximal gain over the longest increasing runs,”
i.e., for Mn(Ln) has been recently derived for the case where X1 has a finite moment of order 3 + ε, ε > 0. Assuming that X1 has a finite mean, we prove for any a = 0, 1, ..., that the s.l.l.n. for M(Ln - a) is equivalent to EX
1
3+a
I{X1 > 0} < ∞. We derive also some new results for the a.s. asymptotics of Ln. Bibliography: 5 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 311, 2004, pp. 179–189. 相似文献
9.
Let {X
i
}
i=1∞ be a standardized stationary Gaussian sequence with covariance function r(n) = EX
1
X
n+1, S
n
= Σ
i=1
n
X
i
, and $\bar X_n = \tfrac{{S_n }}
{n}
$\bar X_n = \tfrac{{S_n }}
{n}
. And let N
n
be the point process formed by the exceedances of random level $(\tfrac{x}
{{\sqrt {2\log n} }} + \sqrt {2\log n} - \tfrac{{\log (4\pi \log n)}}
{{2\sqrt {2\log n} }})\sqrt {1 - r(n)} + \bar X_n
$(\tfrac{x}
{{\sqrt {2\log n} }} + \sqrt {2\log n} - \tfrac{{\log (4\pi \log n)}}
{{2\sqrt {2\log n} }})\sqrt {1 - r(n)} + \bar X_n
by X
1,X
2,…, X
n
. Under some mild conditions, N
n
and S
n
are asymptotically independent, and N
n
converges weakly to a Poisson process on (0,1]. 相似文献
10.
Daniel Wulbert 《Israel Journal of Mathematics》2001,126(1):363-380
LetX be a Borel subset of a separable Banach spaceE. Letμ be a non-atomic,σ-finite, Borel measure onX. LetG ⊆L
1 (X, Σ,μ) bem-dimensional.
Theorem:There is an l ∈ E* and real numbers −∞=x
0<x
1<x
2<…<x
n<x
n+1=∞with n≤m, such that for all g ∈ G,
相似文献
11.
James R. Holub 《Israel Journal of Mathematics》1985,52(3):231-238
LetW(D) denote the set of functionsf(z)=Σ
n=0
∞
A
n
Z
n
a
nzn for which Σn=0
∞|a
n
|<+∞. Given any finite set lcub;f
i
(z)rcub;
i=1
n
inW(D) the following are equivalent: (i) The generalized shift sequence lcub;f
1(z)z
kn
,f
2(z)z
kn+1, …,f
n
(z)z
(k+1)n−1rcub;
k=0
∞
is a basis forW(D) which is equivalent to the basis lcub;z
m
rcub;
m=0
∞
. (ii) The generalized shift sequence is complete inW(D), (iii) The function
has no zero in |z|≦1, wherew=e
2πiti
/n. 相似文献
12.
Henry Teicher 《Journal of Theoretical Probability》1995,8(4):779-793
Conditions are obtained for (*)E|S
T
|γ<∞, γ>2 whereT is a stopping time and {S
n=∑
1
n
,X
j
ℱ
n
,n⩾1} is a martingale and these ensure when (**)X
n
,n≥1 are independent, mean zero random variables that (*) holds wheneverET
γ/2<∞, sup
n≥1
E|X
n
|γ<∞. This, in turn, is applied to obtain conditions for the validity ofE|S
k,T
|γ<∞ and of the second moment equationES
k,T
2
=σ
2
EΣ
j=k
T
S
k−1,j−1
2
where
and {X
n
, n≥1} satisfies (**) and
,n≥1. The latter is utilized to elicit information about a moment of a stopping rule. It is also shown for i.i.d. {X
n
, n≥1} withEX=0,EX
2=1 that the a.s. limit set of {(n log logn)−k/2
S
k,n
,n≥k} is [0,2
k/2/k!] or [−2
k/2/k!] according ask is even or odd and this can readily be reformulated in terms of the corresponding (degenerate kernel)U-statistic
. 相似文献
13.
Let {X
n
; n ≥ 1} be a strictly stationary sequence of negatively associated random variables with mean zero and finite variance. Set
S
n
= Σ
k=1
n
X
k
, M
n
= max
k≤n
|S
k
|, n ≥ 1. Suppose σ
2 = EX
12 + 2Σ
k=2∞ EX
1
X
k
(0 < σ < ∞). In this paper, the exact convergence rates of a kind of weighted infinite series of E{M
n
−σɛ√n log n}+ and E{|S
n
| − σɛ√n log n}+ as ɛ ↘ 0 and E{σɛ√π
2
π/8logn − M
n
}+ as ɛ ↗ ∞ are obtained. 相似文献
14.
Katalin Marton 《Probability Theory and Related Fields》1998,110(3):427-439
Summary. Let X={X
i
}
i
=−∞
∞ be a stationary random process with a countable alphabet and distribution q. Let q
∞(·|x
−
k
0) denote the conditional distribution of X
∞=(X
1,X
2,…,X
n
,…) given the k-length past:
Write d(1,x
1)=0 if 1=x
1, and d(1,x
1)=1 otherwise. We say that the process X admits a joining with finite distance u if for any two past sequences −
k
0=(−
k
+1,…,0) and x
−
k
0=(x
−
k
+1,…,x
0), there is a joining of q
∞(·|−
k
0) and q
∞(·|x
−
k
0), say dist(0
∞,X
0
∞|−
k
0,x
−
k
0), such that
The main result of this paper is the following inequality for processes that admit a joining with finite distance:
Received: 6 May 1996 / In revised form: 29 September 1997 相似文献
15.
Jeremy Berman 《Israel Journal of Mathematics》1978,31(3-4):383-393
Forn≧1, letS
n=ΣX
n,i (1≦i≦r
n <∞), where the summands ofS
n are independent random variables having medians bounded in absolute value by a finite number which is independent ofn. Letf be a nonnegative function on (− ∞, ∞) which vanishes and is continuous at the origin, and which satisfies, for some
for allt≧1 and all values ofx.
Theorem.For centering constants c
n,let S
n
− c
n
converge in distribution to a random variable S. (A)In order that Ef(Sn − cn) converge to a limit L, it is necessary and sufficient that there exist a common limit
(B)If L exists, then L<∞ if and only if R<∞, and when L is finite, L=Ef(S)+R.
Applications are given to infinite series of independent random variables, and to normed sums of independent, identically
distributed random variables. 相似文献
16.
Perturbations of the unit vector basis of the formX
n
=Σ|j−n|≦m
a
nj
e
j
wherem is a fixed positive integer are investigated. It is shown that if |a
nj
|≦1 and if {x
n
} possesses a biorthogonal sequence uniformly bounded inl
p
for some 1<=p<∞, then {x
n
} is a seminormalized basic sequence in some reflexive Orlicz spacel
N, then {xn} is equivalent to {e
n} inl
N. 相似文献
17.
Let {Y
i
;−∞<i<∞} be a doubly infinite sequence of independent random elements taking values in a separable real Banach space and stochastically
dominated by a random variable X. Let {a
i
;−∞<i<∞} be an absolutely summable sequence of real numbers and set V
i
=∑
k=−∞∞
a
i+k
Y
i
,i≥1. In this paper, we derive that if
and E|X|
μ
log
ρ
|X|<0, for some μ (0<μ<2, μ≠1) and ρ>0 then
for all ε>0.
This work was partially supported by the Korean Research Foundation Grant funded by the Korean Government (KRF-2006-353-C00006,
KRF-2006-251-C00026). 相似文献
18.
K. F. Cheng 《Annals of the Institute of Statistical Mathematics》1982,34(1):479-489
Summary Letf
n
(p)
be a recursive kernel estimate off
(p) thepth order derivative of the probability density functionf, based on a random sample of sizen. In this paper, we provide bounds for the moments of
and show that the rate of almost sure convergence of
to zero isO(n
−α), α<(r−p)/(2r+1), iff
(r),r>p≧0, is a continuousL
2(−∞, ∞) function. Similar rate-factor is also obtained for the almost sure convergence of
to zero under different conditions onf.
This work was supported in part by the Research Foundation of SUNY. 相似文献
19.
This paper considers empirical Bayes estimation of the mean θ of the univariate normal densityf
0 with known variance where the sample sizesm(n) may vary with the component problems but remain bounded by
<∞. Let {(θ
n
,X
n
=(X
n,1,...,X
n, m(n)
))} be a sequence of independent random vectors where theθ
n
are unobservable and iidG and, givenθ
n
=θ has densityf
θ
m(n)
. The first part of the paper exhibits estimators for the density of
and its derivative whose mean-squared errors go to zero with rates
and
respectively. LetR
m(n+1)(G) denote the Bayes risk in the squared-error loss estimation ofθ
n+1 usingX
n+1. For given 0<a<1, we exhibitt
n
(X1,...,X
n
;X
n+1) such that
.
forn>1 under the assumption that the support ofG is in [0, 1]. Under the weaker condition that E[|θ|2+γ]<∞ for some γ>0, we exhibitt
n
*
(X
1,...,X
n
;X
n+1) such that
forn>1. 相似文献
20.
Françoise Lust-Piquard 《Potential Analysis》2006,24(1):47-62
Let L=?Δ+|ξ|2 be the harmonic oscillator on $\mathbb{R}^{n}Let L=−Δ+|ξ|2 be the harmonic oscillator on
\mathbbRn\mathbb{R}^{n}
, with the associated Riesz transforms R2j−1=(∂/∂ξj)L−1/2,R2j=ξjL−1/2. We give a shorter proof of a recent result of Harboure, de Rosa, Segovia, Torrea: For 1<p<∞ and a dimension free constant Cp,
||(?k=12n|Rk(f)|2)1/2||Lp(\mathbbRn,dx)\leqslant Cp||f||Lp(\mathbbRn,dx).\bigg\Vert \bigg(\sum_{k=1}^{2n}\vert R_{k}(f)\vert ^{2}\bigg)^{{1}/{2}}\bigg\Vert _{L^{p}(\mathbb{R}^{n},\mathrm{d}\xi )}\leqslant C_{p}\Vert f\Vert _{L^{p}(\mathbb{R}^{n},\mathrm{d}\xi )}. 相似文献
|