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1.
For positive integersn, m and realp≥1, let
Upper and lower bounds for this quantity are derived, extending results of Brown and Spencer forB
1(n,n), corresponding to the Gale-Berlekamp switching problem. For a Minkowski spaceM of dimensionm, define
a quantity investigated by Dvoretzky and Rogers. 相似文献
2.
For a trigonometric series
defined on [−π, π)
m
, where V is a certain polyhedron in R
m
, we prove that
if the coefficients a
k
satisfy the following Sidon-Telyakovskii-type conditions:
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 5, pp. 579–585, May, 2008. 相似文献
3.
Hannelore Liero 《Probability Theory and Related Fields》1989,82(4):587-614
Let (X, Y) be a dx-valued random vector and let r(t)=E(Y/X=t) be the regression function of Y on X that has to be estimated from a sample (X
i, Yi), i=1,..., n. We establish conditions ensuring that an estimate of the form
相似文献
4.
In what follows, $C$ is the space of
-periodic continuous functions; P is a seminorm defined on C, shift-invariant, and majorized by the uniform norm;
is the mth modulus of continuity of a function f with step h and calculated with respect to P;
,
(
),
,
5.
Let {Xni} be an array of rowwise negatively associated random variables and Tnk=k∑i=1 i^a Xni for a ≥ -1, Snk =∑|i|≤k Ф(i/nη)1/nη Xni for η∈(0,1],where Ф is some function. The author studies necessary and sufficient conditions of ∞∑n=1 AnP(max 1≤k≤n|Tnk|〉εBn)〈∞ and ∞∑n=1 CnP(max 0≤k≤mn|Snk|〉εDn)〈∞ for all ε 〉 0, where An, Bn, Cn and Dn are some positive constants, mn ∈ N with mn /nη →∞. The results of Lanzinger and Stadtmfiller in 2003 are extended from the i.i.d, case to the case of the negatively associated, not necessarily identically distributed random variables. Also, the result of Pruss in 2003 on independent variables reduces to a special case of the present paper; furthermore, the necessity part of his result is complemented. 相似文献
6.
Xia Chen 《Journal of Theoretical Probability》1999,12(2):421-445
Let {X
n
}
n0 be a Harris recurrent Markov chain with state space E, transition probability P(x, A) and invariant measure , and let f be a real measurable function on E. We prove that with probability one,
7.
Estimates for deviations are established for a large class of linear methods of approximation of periodic functions by linear combinations of moduli of continuity of different orders. These estimates are sharp in the sense of constants in the uniform and integral metrics. In particular, the following assertion concerning approximation by splines is proved: Suppose that
is odd,
. Then
8.
Francesco Leonetti 《Annali dell'Universita di Ferrara》1985,31(1):169-184
Riassunto In questo lavoro si prova la regolarità h?lderiana delle derivate, fino all'ordinek, dei minimi locali
dei funzionali
sotto opportune ipotesi suA
ij
αβ
e sug.
Summary In this paper we prove h?lder-continuity of the derivates, up to orderk, of local minima of functionals under suitable hypotheses forA ij αβ andg.相似文献 9.
Summary Let {X
ij; i>0, j>0} be a double sequence of i.i.d. random variables taking values in the d-dimensional integer lattice E
d
. Also let
. Then the range of random walk {S
mn: m>0, n>0} up to time (m, n), denoted by R
mn
, is the cardinality of the set {S
pq: 0
10.
A celebrated result of Johnson, Maurey, König and Retherford from 1977 states that for
every complex
matrix
satisfies the following eigenvalue estimate:
11.
Let X
1, X
2,... denote an i.i.d. sequence of real valued random variables which ly in the domain of attraction of a stable law Q with index 0<1. under=" a=" von=" mises=" condition=" we=" show=" that=" the=" sum=" of=" order=" statistics=">1.>
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