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1.
Andreas Maurer 《Random Structures and Algorithms》2006,29(2):121-138
Following the entropy method this paper presents general concentration inequalities, which can be applied to combinatorial optimization and empirical processes. The inequalities give improved concentration results for optimal traveling salesmen tours, Steiner trees, and the eigenvalues of random symmetric matrices. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2006 相似文献
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V. V. Gorodetskii 《Journal of Mathematical Sciences》1984,24(5):501-509
Let be a stationary Gaussian sequence,, One proves an invariance principle for. One obtains also a representation of the limiting process in the form of a stochastic integral.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 97, pp. 32–44, 1980.The author expresses his deep gratitude to Yu. A. Davydov for useful discussions. 相似文献
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Let = (1,...,d) be a vector with positive components and let D be the corresponding mixed derivative (of order j with respect to the jth variable). In the case where d > 1 and 0 < k < r are arbitrary, we prove that
and
for all
Moreover, if
is the least possible value of the exponent in this inequality, then
Deceased.Translated from Ukrainskyi Matematychnyi Zhurnal, Vol. 56, No. 5, pp. 579–594, May, 2004. 相似文献
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We prove a new exact Kolmogorov-type inequality estimating the norm of a mixed fractional-order derivative (in Marchaud's
sense) of a function of two variables via the norm of the function and the norms of its partial derivatives of the first order.
Translated from Ukrains'kyi Matematchnyi Zhurnal, Vol. 60, No. 6, pp. 837–842, June, 2008. 相似文献
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The paper deals with some linear as well as some non-linear generalizations of integral inequalities of Bellman-Bihari type for functions of several variables when the integration domain is a parallelepiped. 相似文献
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Georg Lindgren 《Stochastic Processes and their Applications》1984,17(2):285-312
The exit rate from a ‘safe region’ plays an important role in dynamic reliability theory with multivariate random loads. For Gaussian processes the exit rate is simply calculated only for spherical or linear boundaries. However, many smooth boundaries, not of any of these types, are asymptotically spherical in variables of lower dimension, having a greater curvature in the remaining variables. As is shown in this paper, the asymptotic exit rate is then simply expressed as the exit rate from a sphere for a process of the lower dimensions, corrected by an explicit factor.The procedure circumvents the need to calculate complicated exit rate integrals for general boundaries, reducing the problem to a Gaussian probability integral for independent variables.A result of independent interest relates the tail distribution for a sum of a noncentral χ2-variable and a weighted sum of squares of noncentral normal variables, to the tail distribution of the χ2-variable only. 相似文献
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We investigate the correlation between the constants K(ℝn) and
, where
is the exact constant in a Kolmogorov-type inequality, ℝ is the real straight line,
, L
l
p, p
(G
n) is the set of functions ƒ ∈ L
p
(G
n
) such that the partial derivative
belongs to L
p
(G
n
),
, 1 ≤ p ≤ ∞, l ∈ ℕn, α ∈ ℕ
0
n
= (ℕ ∪ 〈0〉)n, D
α
f is the mixed derivative of a function ƒ, 0 < μi < 1,
, and ∑
i=0
n
. If G
n
= ℝ, then μ0=1−∑
i=0
n
(α
i
/l
i
), μi = αi/l
i
,
if
, then μ0=1−∑
i=0
n
(α
i
/l
i
) − ∑
i=0
n
(λ/l
i
), μi = αi/ l
i
+ λ/l
i
,
, λ ≥ 0. We prove that, for λ = 0, the equality
is true.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 5, pp. 597–606, May, 2006. 相似文献
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Qiman Shao 《应用数学学报(英文版)》1990,6(4):338-350
This paper contains the Kolmogorov-Prokhorov exponential inequalities for dependent random variables, i.e., for-mixing,-mixing and-mixing. As an application, the law of iterated logarithm is established for stationary-mixing sequence under a nearly best assumption.Research supported by National Science Foundation Grant. 相似文献
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《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(3-4):283-293
A prophet inequality with constant a satisfying K-log K=2 is obtained for a class dependent random variables in the full information case, under the same assumptions the prophet constant 4 is obtained in the partial information case. Applications to sums of independent random variables are given 相似文献
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Some inequalities for Gaussian processes and applications 总被引:3,自引:0,他引:3
Yehoram Gordon 《Israel Journal of Mathematics》1985,50(4):265-289
We present a generalization of Slepian's lemma and Fernique's theorem. We show how these can be easily applied to give a new
proof, with improved estimates, of Dvoretzky’s theorem on the existence of “almost” spherical sections for arbitrary convex
bodies inR
N, while avoiding the isoperimetric inequality.
Supported by Technion V.P.R. grant #100–526, and fund for the promotion of research at the Technion #100–559. 相似文献
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M. I. Tsatsulin 《Mathematical Notes》1991,50(2):872-875
Translated from Matematicheski Zametki, Vol. 50, No. 2, pp. 146–151, August, 1991. 相似文献
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Chin-Yuan Hu 《Journal of Mathematical Analysis and Applications》2005,309(1):336-352
In a recent paper, Matysiak and Szablowski [V. Matysiak, P.J. Szablowski, Theory Probab. Appl. 45 (2001) 711-713] posed an interesting conjecture about a lower bound of real-valued characteristic functions. Under a suitable moment condition on distributions, we prove the conjecture to be true. The unified approach proposed here enables us to obtain new inequalities for characteristic functions. We also show by example that the improvement in the bounds is significant if more information about the distribution is available. 相似文献