共查询到20条相似文献,搜索用时 15 毫秒
1.
We consider different kinds of convergence of homogeneous polynomials and multilinear forms in random variables. We show that for a variety of complex random variables, the almost sure convergence of the polynomial is equivalent to that of the multilinear form, and to the square summability of the coefficients. Also, we present polynomial Khintchine inequalities for complex gaussian and Steinhaus variables. All these results have no analogues in the real case. Moreover, we study the Lp-convergence of random polynomials and derive certain decoupling inequalities without the usual tetrahedral hypothesis. We also consider convergence on “full subspaces” in the sense of Sjögren, both for real and complex random variables, and relate it to domination properties of the polynomial or the multilinear form, establishing a link with the theory of homogeneous polynomials on Banach spaces. 相似文献
2.
甘师信 《数学物理学报(A辑)》2010,30(2):327-334
该文证明了一类B值随机元序列的Rosenthal不等式,一些经典的Rosenthal不等式作为其推论被蕴含其中.作为不等式的应用,还给出了行为鞅差随机元的阵列的完全收敛性的一些结果,推广和改进了一些熟知的结论. 相似文献
3.
Kewei Zhang 《Journal of Mathematical Analysis and Applications》2002,271(1):288-296
We establish an inequality for symmetric bilinear forms involving both the norm and the inner product of vectors. We use the inequality to convert known inequalities in real Hilbert spaces such as classical Hilbert's inequality to sharper inequalities. 相似文献
4.
A. N. Chuprunov 《Journal of Mathematical Sciences》1997,83(3):381-392
We deal with independent random variables which are the values of a stochastic process taken at random points in time. So
we have random variables depending upon a random parameter. We obtain the conditions providing the weak convergence of random
lines defined by sums or maxima or bilinear forms of these random variables for almost all values of the parameter, to one
and the same stochastic process. These limit stochastic processes are described.
Proceedings of the XVII Seminar on Stability Problems for Stochastic Models, Kazan, Russia, 1995, Part II. 相似文献
5.
This paper is devoted to the study of Φ-moment inequalities for noncommutative martingales. In particular, we prove the noncommutative Φ-moment analogues of martingale transformations, Stein’s inequalities, Khintchine’s inequalities for Rademacher’s random variables, and Burkholder–Gundy’s inequalities. The key ingredient is a noncommutative version of Marcinkiewicz type interpolation theorem for Orlicz spaces which we establish in this paper. 相似文献
6.
Dave Witte Akihiko Yukie Roger Zierau 《Transactions of the American Mathematical Society》2000,352(4):1687-1708
We apply M. Ratner's theorem on closures of unipotent orbits to the study of three families of prehomogeneous vector spaces. As a result, we prove analogues of the Oppenheim Conjecture for simultaneous approximation by values of certain alternating bilinear forms in an even number of variables and certain alternating trilinear forms in six and seven variables.
7.
Oleg N. German 《Proceedings of the Steklov Institute of Mathematics》2011,275(1):216-228
We prove inequalities for multiplicative analogues of Diophantine exponents; these inequalities are similar to the ones known
in the classical case. Particularly, we show that a matrix is badly approximable if and only if its transpose is badly approximable
and establish some inequalities connecting multiplicative exponents with ordinary ones. 相似文献
8.
Jan Maas 《Journal of Mathematical Analysis and Applications》2010,363(2):383-398
We develop a theory of Malliavin calculus for Banach space-valued random variables. Using radonifying operators instead of symmetric tensor products we extend the Wiener-Itô isometry to Banach spaces. In the white noise case we obtain two sided Lp-estimates for multiple stochastic integrals in arbitrary Banach spaces. It is shown that the Malliavin derivative is bounded on vector-valued Wiener-Itô chaoses. Our main tools are decoupling inequalities for vector-valued random variables. In the opposite direction we use Meyer's inequalities to give a new proof of a decoupling result for Gaussian chaoses in UMD Banach spaces. 相似文献
9.
In this paper we study the computation of symmetric systems of bilinear forms over finite fields via symmetric bilinear algorithms. We show that, in general, the symmetric complexity of a system is upper bounded by a constant multiple of the bilinear complexity; we characterize symmetric algorithms in terms of the cosets of a specific cyclic code, and we show that the problem of finding an optimal symmetric algorithm is equivalent to the maximum-likelihood decoding problem for this code. 相似文献
10.
We obtain probability combinatorial inequalities for independent random variables, strengthening the well-known Rosenthal inequality. As a corollary, we prove that the generalized Rosenthal inequality for identically distributed independent functions remains valid in the case of quasinormed symmetric spaces. 相似文献
11.
Some Kolmogorov probability inequalities for quadratic forms and weighted quadratic forms of negative superadditive dependent (NSD) uniformly bounded random variables are provided. Using these inequalities, some complete convergence of randomized quadratic forms under some suitable conditions are evaluated. Moreover, various examples are presented in which the given conditions of our results are satisfied. 相似文献
12.
From the ordinary notion of negative association for a sequence of random variables, a new concept called conditional negative
association is introduced. The relation between negative association and conditional negative association is answered, that
is, the negative association does not imply the conditional negative association, and vice versa. The basic properties of
conditional negative association are developed, which extend the corresponding ones under the non-conditioning setup. By means
of these properties, some Rosenthal type inequalities for maximum partial sums of such sequences of random variables are derived,
which extend the corresponding results for negatively associated random variables. As applications of these inequalities,
some conditional mean convergence theorems, conditionally complete convergence results and a conditional central limit theorem
stated in terms of conditional characteristic functions are established. In addition, some lemmas in the context are of independent
interest. 相似文献
13.
《数学季刊》2014,(2)
Some probability inequalities are established for extended negatively dependent(END) random variables. The inequalities extend some corresponding ones for negatively associated random variables and negatively orthant dependent random variables. By using these probability inequalities, we further study the complete convergence for END random variables. We also obtain the convergence rate O(n-1/2ln1/2n) for the strong law of large numbers, which generalizes and improves the corresponding ones for some known results. 相似文献
14.
《Journal of Functional Analysis》2023,284(5):109798
We establish distributional estimates for noncommutative martingales, in the sense of decreasing rearrangements of the spectra of unbounded operators, which generalises the study of distributions of random variables. Our results include distributional versions of the noncommutative Stein, dual Doob, martingale transform and Burkholder-Gundy inequalities. Our proof relies upon new and powerful extrapolation theorems. As an application, we obtain some new martingale inequalities in symmetric quasi-Banach operator spaces and some interesting endpoint estimates. Our main approach demonstrates a method to build the noncommutative and classical probabilistic inequalities in an entirely operator theoretic way. 相似文献
15.
Invariant symmetric bilinear forms for reflection groups 总被引:1,自引:0,他引:1
In this paper we describe a connection between Vinberg's criterion for the existence of an invariant symmetric bilinear form
for a geometric representation of a Coxeter groups and other criteria which are formulated in terms of conjugation invariant
sets of reflections generating a given group. Similar methods lead to the result that every non-symmetrizable Kac--Moody Lie
algebra contains a non-symmetrizable subalgebra of rank 3. Finally we explain how the results for symmetric bilinear forms
can also be obtained for skew-symmetric forms.
Received 3 March 2000. 相似文献
16.
本文讨论赋值环上的对称线性型、二次型和对称矩阵的合同标准形。 相似文献
17.
Anatoly G. Kusraev 《Journal of Mathematical Analysis and Applications》2011,374(1):282-289
A transfer principle from inequalities with inner products to inequalities containing positive semidefinite symmetric bilinear operators with values in a vector lattices is proved. Some applications are also given. 相似文献
18.
O. A. Ivanov 《Journal of Mathematical Sciences》1982,19(3):1250-1253
In this paper we describe a construction, associating with a pair of integral symmetric bilinear forms with identical discriminant forms, an integral symmetric unimodular bilinear form.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 83, pp. 63–66, 1979. 相似文献
19.
This paper presents a general convergence analysis of numericalmethods for solving ordinary differential equations and non-linerVolterra integral and integrodifferential euqations. The conceptof analytic and discrete forms is introduced, Prolongation andrestriction operators reduce the problem of comparing the fundamentalforms. Integral inequalities and their discrete analogues proofof a collocation method for solving Volterra integral equationsof the second kind. 相似文献