共查询到10条相似文献,搜索用时 109 毫秒
1.
Julius Damarackas 《Lithuanian Mathematical Journal》2017,57(4):421-432
We consider the partial-sum process \( {S}_n(t)={\sum}_{k=0}^{\left\lfloor nt\right\rfloor }{X}_k \) of linear processes \( {X}_n={\sum}_{i=0}^{\infty }{c}_i{\upxi}_{n-i} \) with independent identically distributed innovations {ξ i } belonging to the domain of attraction of α-stable law (0 < α ≤ 2). If |c k |?=?k ?γ?,?k?∈???,?γ?> max(1, 1/α), and \( {\sum}_{k=0}^{\infty}\kern0.5em ck=0 \) (the case of negative memory for the stationary sequence {X n }), then it is known that the normalizing sequence of S n (1) can grow as n 1/α?γ+1 or remain bounded if the signs of the coefficients are constant or alternate, respectively. It is of interest to know whether it is possible, given ? ∈ (0, 1/α ? γ + 1), to change the signs of c k so that the rate of growth of the normalizing sequence would be n ? . In this paper, we give the positive answer: we propose a way of choosing the signs and investigate the finite-dimensional convergence of appropriately normalized S n (t) to linear fractional Lévy motion. 相似文献
2.
Youri Davydov 《Lithuanian Mathematical Journal》2011,51(2):171-179
Let X i = {X i (t), t ∈ T} be i.i.d. copies of a centered Gaussian process X = {X(t), t ∈ T} with values in\( {\mathbb{R}^d} \) defined on a separable metric space T. It is supposed that X is bounded. We consider the asymptotic behavior of convex hullsand show that, with probability 1,(in the sense of Hausdorff distance), where the limit shape W is defined by the covariance structure of X: W = conv{K t , t ∈ T}, Kt being the concentration ellipsoid of X(t). We also study the asymptotic behavior of the mathematical expectations E f(W n ), where f is an homogeneous functional.
相似文献
$ {W_n} = {\text{conv}}\left\{ {{X_1}(t), \ldots, {X_n}(t),\,\,t \in T} \right\} $
$ \mathop {{\lim }}\limits_{n \to \infty } \frac{1}{{\sqrt {{2\ln n}} }}{W_n} = W $
3.
András Hajnal István Juhász Lajos Soukup Zoltán Szentmiklóssy 《Acta Mathematica Hungarica》2011,131(3):230-274
\(f\: \cup {\mathcal {A}}\to {\rho}\) is called a conflict free coloring of the set-system\({\mathcal {A}}\)(withρcolors) if The conflict free chromatic number\(\operatorname {\chi _{\rm CF}}\, ({\mathcal {A}})\) of \({\mathcal {A}}\) is the smallest ρ for which \({\mathcal {A}}\) admits a conflict free coloring with ρ colors.
$\forall A\in {\mathcal {A}}\ \exists\, {\zeta}<{\rho} (|A\cap f^{-1}\{{\zeta}\}|=1).$
\({\mathcal {A}}\) is a (λ,κ,μ)-system if \(|{\mathcal {A}}| = \lambda\), |A|=κ for all \(A \in {\mathcal {A}}\), and \({\mathcal {A}}\) is μ-almost disjoint, i.e. |A∩A′|<μ for distinct \(A, A'\in {\mathcal {A}}\). Our aim here is to study for λ≧κ≧μ, actually restricting ourselves to λ≧ω and μ≦ω.
For instance, we prove that$\operatorname {\chi _{\rm CF}}\, (\lambda,\kappa,\mu) = \sup \{\operatorname {\chi _{\rm CF}}\, ({\mathcal {A}})\: {\mathcal {A}}\mbox{ is a } (\lambda,\kappa,\mu)\mbox{-system}\}$
? for any limit cardinal κ (or κ=ω) and integers n≧0, k>0, GCH implies
? if λ≧κ≧ω>d>1, then λ<κ +ω implies \(\operatorname {\chi _{\rm CF}}\, (\lambda,\kappa,d) <\omega\) and λ≧? ω (κ) implies \(\operatorname {\chi _{\rm CF}}\, (\lambda,\kappa,d) = \omega\);? GCH implies \(\operatorname {\chi _{\rm CF}}\, (\lambda,\kappa,\omega) \le \omega_{2}\) for λ≧κ≧ω 2 and V=L implies \(\operatorname {\chi _{\rm CF}}\, (\lambda,\kappa,\omega) \le \omega_{1}\) for λ≧κ≧ω 1;? the existence of a supercompact cardinal implies the consistency of GCH plus \(\operatorname {\chi _{\rm CF}}\,(\aleph_{\omega+1},\omega_{1},\omega)= \aleph_{\omega+1}\) and \(\operatorname {\chi _{\rm CF}}\, (\aleph_{\omega+1},\omega_{n},\omega) = \omega_{2}\) for 2≦n≦ω;? CH implies \(\operatorname {\chi _{\rm CF}}\, (\omega_{1},\omega,\omega) = \operatorname {\chi _{\rm CF}}\, (\omega_{1},\omega_{1},\omega) = \omega_{1}\), while \(MA_{\omega_{1}}\) implies \(\operatorname {\chi _{\rm CF}}\, (\omega_{1},\omega,\omega) = \operatorname {\chi _{\rm CF}}\, (\omega_{1},\omega_{1},\omega) = \omega\). 相似文献
$\operatorname {\chi _{\rm CF}}\, (\kappa^{+n},t,k+1) =\begin{cases}\kappa^{+(n+1-i)}&; \text{if \ } i\cdot k < t \le (i+1)\cdot k,\ i =1,\dots,n;\\[2pt]\kappa&; \text{if \ } (n+1)\cdot k < t;\end{cases}$
4.
G. G. Gevorkyan K. A. Navasardyan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2017,52(3):149-160
In this paper we obtain a necessary and sufficient condition on the sequence of natural numbers {q n } such that the almost everywhere convergence of the cubic partial sums S qn (x) of the multiple Haar series Σn a nχn(x) and the condition lim inf \(\lambda \cdot mes\left\{ {x:\begin{array}{*{20}{c}} {\sup } \\ n \end{array}\left| {S{}_{qn}\left( x \right)} \right| \succ \lambda } \right\} = 0\), imply that the coefficients a n can be uniquely determined by the sum of the series. Also, we have obtained a necessary and sufficient condition for the series \(\sum\limits_{n = 1}^\infty {{\varepsilon _n}{a_n}} {\chi _n}\left( x \right)\) with an arbitrary bounded sequence {ε n} to be a Fourier-Haar series of an A-integrable function. 相似文献
5.
Maxim Vsemirnov 《中国科学 数学(英文版)》2018,61(11):2101-2110
Consider the sequence of algebraic integers un given by the starting values u0 = 0, u1 = 1 and the recurrence \(u_{n+1}=(4\rm{cos}^2(2\pi/7)-1)\it{u}_{n}-u_{n-\rm{1}}\). We prove that for any n ? {1, 2, 3, 5, 8, 12, 18, 28, 30} the n-th term of the sequence has a primitive divisor in \(\mathbb{Z}[2\rm{cos}(2\pi/7)]\). As a consequence we deduce that for any suffciently large n there exists a prime power q such that the group PSL2(q) can be generated by a pair x, y with \(x^2=y^3=(xy)^7=1\) and the order of the commutator [x, y] is exactly n. The latter result answers in affrmative a question of Holt and Plesken. 相似文献
6.
Let {X n }n?≥?1 be a sequence of strictly stationary m-dependent random variableswith EX1 = 0 and \( \mathrm{E}{X}_1^2<\infty \), and let (b n ) be an increasing sequence of positive numbers such that b n ?↑?∞ and \( {b}_n/\sqrt{n}\downarrow 0\kern0.5em \mathrm{as}\kern0.5em n\to \infty \). We establish a moderate deviation principle of \( {\left({b}_n\sqrt{n}\right)}^{-1}{\sum}_{i=1}^n{X}_i \) under the condition
which is weaker than the classical exponential integrability condition. The results in the present paper weaken the assumptions of Chen [5] and extend partially the results of Eichelsbacher and Löwe [10]. 相似文献
$$ \underset{n\to \infty }{\lim \sup}\frac{1}{b_n^2}\log \left[n\mathbf{P}\left(\left|{X}_1\right|>{b}_n\sqrt{n}\right)\right]=-\infty, $$
7.
Expansions for the distribution and the maximum from distributions with an asymptotically gamma tail when a trend is present 下载免费PDF全文
We give expansions about the Gumbel distribution in inverse powers of n and log n for Mn, the maximum of a sample size n or n + 1 when the j-th observation is μ(j/n) + ej, μ is any smooth trend function and the residuals {ej } are independent and identically distributed with P(e r) ≈ exp(-δx)xd0∑∞k=1ckx-kβ as x →∞. We illustrate practical value of the expansions using simulated data sets. 相似文献
8.
Alexander Koldobsky 《Archiv der Mathematik》2011,97(1):91-98
We prove the stability of the affirmative part of the solution to the complex Busemann–Petty problem. Namely, if K and L are origin-symmetric convex bodies in \({{\mathbb C}^n}\), n = 2 or n = 3, \({\varepsilon >0 }\) and \({{\rm Vol}_{2n-2}(K\cap H) \le {\rm Vol}_{2n-2}(L \cap H) + \varepsilon}\) for any complex hyperplane H in \({{\mathbb C}^n}\) , then \({({\rm Vol}_{2n}(K))^{\frac{n-1}n}\le({\rm Vol}_{2n}(L))^{\frac{n-1}n} + \varepsilon}\) , where Vol2n is the volume in \({{\mathbb C}^n}\) , which is identified with \({{\mathbb R}^{2n}}\) in the natural way. 相似文献
9.
T. R. Muradov 《Doklady Mathematics》2012,85(2):219-221
In this paper, the system of exponents \(\{ e^{i\lambda _n t} \} _{n \in Z} \) is considered, where {λ n } ? R has the following asymptotic form: λ n = n ? α sign n + O(|n|?β). Basis properties of this system in Lebesgue space with variable summability factor are investigated. 相似文献
10.
Let {Z u = ((εu, i, j))p×n} be random matrices where {εu, i, j} are independently distributed. Suppose {A i }, {B i } are non-random matrices of order p × p and n × n respectively. Consider all p × p random matrix polynomials \(P = \prod\nolimits_{i = 1}^{k_l } {\left( {n^{ - 1} A_{t_i } Z_{j_i } B_{s_i } Z_{j_i }^* } \right)A_{t_{k_l + 1} } }\). We show that under appropriate conditions on the above matrices, the elements of the non-commutative *-probability space Span {P} with state p?1ETr converge. As a by-product, we also show that the limiting spectral distribution of any self-adjoint polynomial in Span{P} exists almost surely. 相似文献