共查询到20条相似文献,搜索用时 296 毫秒
1.
If a setX ⊂E
n has non-emptyk-dimensional interior, or if some point isk-dimensional surrounded, then the classic theorem of E. Steinitz may be extended. For example ifX ⊂E
n has int
k
X ≠ 0, (0 ≦k≦n) and ifp ɛ int conX, thenp ɛ int conY for someY ⊂X with cardY≦2n−k+1. 相似文献
2.
Harry Kesten 《Israel Journal of Mathematics》1979,32(1):83-96
LetX
n, n≧0, be a martingale with respect to the σ-fieldsF
n
and letB
n
2
=Σ1≧n
E{(X
1−X
1−1)2|F
1−1} It is known that ifB
1
2
<∞ on some set Ω0 thenX
∞=limX
n exists and is finite a.e. on Ω0 We show that under suitable conditions there exists a constant ν<∞ for which lim supB
n
−1
{log logB
n
2
}−1/2|X
∞−X
n−1
| ≦ √2(η+1). If “the fluctuations ofB
n are small” (in the sense of the Corollary) then ν=0 and the usual upper bound of a law of the iterated logrithm results.
This upper bound is not necessarily achieved, though.
Research supported in part by the NSF under Grant No. MCS 72-04534A04. 相似文献
3.
LU Chuanrong QIU Jin & XU Jianjun School of Mathematics Statistics Zhejiang University of Finance Economics Hangzhou China Department of Mathematics Zhejiang University Hangzhou China 《中国科学A辑(英文版)》2006,49(12):1788-1799
Let {Xn,-∞< n <∞} be a sequence of independent identically distributed random variables with EX1 = 0, EX12 = 1 and let Sn =∑k=1∞Xk, and Tn = Tn(X1,…,Xn) be a random function such that Tn = ASn Rn, where supn E|Rn| <∞and Rn = o(n~(1/2)) a.s., or Rn = O(n1/2-2γ) a.s., 0 <γ< 1/8. In this paper, we prove the almost sure central limit theorem (ASCLT) and the function-typed almost sure central limit theorem (FASCLT) for the random function Tn. As a consequence, it can be shown that ASCLT and FASCLT also hold for U-statistics, Von-Mises statistics, linear processes, moving average processes, error variance estimates in linear models, power sums, product-limit estimators of a continuous distribution, product-limit estimators of a quantile function, etc. 相似文献
4.
Beata Randrianantoanina 《Israel Journal of Mathematics》1999,113(1):45-60
We show that the Rudin-Plotkin isometry extension theorem inL
pimplies that whenX andY are isometric subspaces ofL
pandp is not an even integer, 1≤p<∞, thenX is complemented inL
pif and only ifY is; moreover, the constants of complementation ofX andY are equal. We provide examples demonstrating that this fact fails whenp is an even integer larger than 2. 相似文献
5.
S. J. Dilworth 《Israel Journal of Mathematics》1985,52(1-2):15-27
Suppose that 1<p≦2, 2≦q<∞. The formal identity operatorI:l
p→l
qfactorizes through any given non-compact operator from ap-smooth Banach space into aq-convex Banach space. It follows that ifX is a 2-convex space andY is an infinite dimensional subspace ofX which is isomorphic to a Hilbert space, thenY contains an isomorphic copy ofl
2 which is complemented inX. 相似文献
6.
Let E be a cookie-cutter set with dimH E =s. It is known that the Hausdorff s-measure and the packing s-measure of the set E are positive and finite. In this paper, we prove that for a gauge function g the set E has positive and finite Hausdorff g-measure if and only if 0 〈 liminft→0 g(t)/ts 〈 ∞. Also, we prove that for a doubling gauge function g the set E has positive and finite packing g-measure if and only if 0 〈 lim supt→0 g(t)/ts 〈 ∞. 相似文献
7.
Louis Halle Rowen 《Israel Journal of Mathematics》1974,18(1):65-74
Let Ω[ξ] denote the polynomial algebra (with 1) in commutative indeterminates {ie65-1}, 1 ≦i, j ≦n, 1 ≦k < ∞, over a commutative ring Ω. Thealgebra of generic matrices Ω [Y] is defined to be the Ω-subalgebra ofM
n (Ω[ξ]) generated by the matricesY
k=({ie65-2}), 1 ≦i, j ≦n, 1 ≦k < ∞. This algebra has been studied extensively by Amitsur and by Procesi in particular Amitsur has used it to construct a
finite dimensional, central division algebra Ω (Y) which is not a crossed product. In this paper we shall prove, for Ω a domain, that Ω(Y) has exponentn in the Brauer group (Amitsur may already know this fact); consequently, for Ω an infinite field andn a multiple of 4, iff(X
1, …,X
m) is a polynomial linear in all theX
i but one (similar to Formanek’s central polynomials for matrix rings) andf
2 is central forM
n (Ω), thenf is central forM
n (Ω). (The existence of a polynomial not central forM
n (Ω), but whose square is central forM
n(Ω) is equivalent to every central division algebra of degreen containing a quadratic extension of its center; well-known theory immediately shows this is the case of 4‖n and 8χn.) Also, information is obtained about Ω(Y) for arbitary Ω, most notably that the Jacobson radical is the set of nilpotent elements.
Partial support for this work was provided by National Science Foundation grant NSF-GP 33591. 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.
S. S. Sinelnikov 《Moscow University Mathematics Bulletin》2011,66(4):158-162
For a Lévy process X = (X
t
)0≤t<∞ we consider the time θ = inf{t ≥ 0: sup
s≤t
X
s
= sup
s≥0
X
s
}. We study an optimal approximation of the time θ using the information available at the current instant. A Lévy process being a combination of a Brownian motion with a drift
and a Poisson process is considered as an example. 相似文献
10.
Adam Osękowski 《Journal of Theoretical Probability》2011,24(3):849-874
In the paper we determine, for any K>0 and α∈[0,1], the optimal constant L(K,α)∈(0,∞] for which the following holds: If X is a nonnegative submartingale and Y is α-strongly differentially subordinate to X, then
supt\mathbbE|Yt| £ Ksupt\mathbbEXtlog+Xt+L(K,a).\sup_t\mathbb{E}|Y_t|\leq K\sup_t\mathbb{E}X_t\log^+X_t+L(K,\alpha). 相似文献
11.
We prove that a Markov operatorT onL
1 has an invariant density if and only if there exists a densityf that satisfies lim sup
n→∞‖T
n
f − f‖ < 2. Using this result, we show that a Frobenius-Perron operatorP is mean ergodic if and only if there exists a densityw such that lim sup
n→∞ ‖P
n
f − w‖<2 for every densityf. Corresponding results hold for strongly continuous semigroups. 相似文献
12.
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
13.
Wolfgang Lusky 《Israel Journal of Mathematics》2004,143(1):239-251
LetX be a Banach space with a sequence of linear, bounded finite rank operatorsR
n:X→X such thatR
nRm=Rmin(n,m) ifn≠m and lim
n→∞
R
n
x=x for allx∈X. We prove that, ifR
n−Rn
−1 factors uniformly through somel
p and satisfies a certain additional symmetry condition, thenX has an unconditional basis. As an application, we study conditions on Λ ⊂ ℤ such thatL
Λ=closed span
, where
, has an unconditional basis. Examples include the Hardy space
. 相似文献
14.
Nicole Tomczak-Jaegermann 《Israel Journal of Mathematics》1984,48(2-3):249-254
ItE is a symmetric Banach sequence which isq-concave with the constant equal to 1 (where 2≦q<∞), thenS
E isq-PL-convex. IfE isq-concave andp-convex with the constants equal to 1 (where 1<p≦2≦q<∞), thenS
E is uniformly convex with modulus of convexity of power typeq and uniformly smooth with modulus of smoothness of power typep. 相似文献
15.
Steven F. Bellenot 《Israel Journal of Mathematics》1981,39(3):234-246
It is shown that for every non-reflexive Banach spaceX withX
**/X reflexive there exists a uniformly bounded sequence of projections {P
n
}
n=1
∞
whose ranges are uniformly isomorphic to {l
p
n
}
n = 1
∞
either forp=1, orp=2 or forp=∞. The proof uses knowledge of the transfinite dualX
ω, ESA Schauder decompositions and proof of a similar statement for spaces with an unconditional basis due to Tzafriri. 相似文献
16.
Yaar Solomon 《Israel Journal of Mathematics》2011,181(1):445-460
We show that any primitive substitution tiling of ℝ2 creates a separated net which is biLipschitz to ℤ2. Then we show that if H is a primitive Pisot substitution in ℝ
d
, for every separated net Y, that corresponds to some tiling τ ∈ X
H
, there exists a bijection Φ between Y and the integer lattice such that sup
y∈Y
∥Φ(y) − y∥ < ∞. As a corollary, we get that we have such a Φ for any separated net that corresponds to a Penrose Tiling. The proofs
rely on results of Laczkovich, and Burago and Kleiner. 相似文献
17.
Carsten Schütt 《Israel Journal of Mathematics》1978,30(3):207-212
The relations of the projection constant λ(E) and the isomorphic distance d(E, 1
n
∞
) of finite-dimensional spacesE whose unconditional basis constant is 1 are investigated. It turns out that both are proportional to the norm of a certain
vector inE. 相似文献
18.
LetX be a Banach space and letA be the infinitesimal generator of a differentiable semigroup {T(t) |t ≥ 0}, i.e. aC
0-semigroup such thatt ↦T(t)x is differentiable on (0, ∞) for everyx εX. LetB be a bounded linear operator onX and let {S(t) |t ≥ 0} be the semigroup generated byA +B. Renardy recently gave an example which shows that {S(t) |t ≥ 0} need not be differentiable. In this paper we give a condition on the growth of ‖T′(t)‖ ast ↓ 0 which is sufficient to ensure that {S(t) |t ≥ 0} is differentiable. Moreover, we use Renardy’s example to study the optimality of our growth condition. Our results can
be summarized roughly as follows:
19.
John Elton 《Israel Journal of Mathematics》1981,40(3-4):255-258
It is proved that if Σ
i=1
∞
X
i
is a non-convergent series in a Banach spaceX such that Σ
i=1
∞
|f(X
i
)|<∞ for all extreme pointsf of the unit ball ofX*, thenX contains a subspace isomorphic toc
0, improving a result of Bessaga and Pelczynski. The proof uses Fonf’s result that Lindenstrauss-Phelps spaces contain isomorphs
ofc
0.
Supported in part by NSF-MCS-8002393. 相似文献
20.
We prove that for every abelian groupG and every compactumX with dim
G
X ≤n ≥ 2 there is aG-acyclic resolutionr:Z→X from a compactumZ with dim
G
Z≤n and dimZ≤n+1 ontoX. 相似文献
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