共查询到20条相似文献,搜索用时 31 毫秒
1.
The generalized maximal operator M in martingale spaces is considered. For 1 < p ≤ q < ∞, the authors give a necessary and sufficient condition on the pair ([^(m)]\hat \mu , v) for M to be a bounded operator from martingale space L
p
(v) into L
q
([^(m)]\hat \mu ) or weak-L
q
([^(m)]\hat \mu ), where [^(m)]\hat \mu is a measure on Ω × ℕ and v a weight on Ω. Moreover, the similar inequalities for usual maximal operator are discussed. 相似文献
2.
Tomohito Naito Kohei Asai Tomoyuki Amano Masanobu Taniguchi 《Statistical Inference for Stochastic Processes》2010,13(3):163-174
In this paper, we propose a local Whittle likelihood estimator for spectral densities of non-Gaussian processes and a local
Whittle likelihood ratio test statistic for the problem of testing whether the spectral density of a non-Gaussian stationary
process belongs to a parametric family or not. Introducing a local Whittle likelihood of a spectral density f
θ
(λ) around λ, we propose a local estimator [^(q)] = [^(q)] (l){\hat{\theta } = \hat{\theta } (\lambda ) } of θ which maximizes the local Whittle likelihood around λ, and use f[^(q)] (l) (l){f_{\hat{\theta } (\lambda )} (\lambda )} as an estimator of the true spectral density. For the testing problem, we use a local Whittle likelihood ratio test statistic
based on the local Whittle likelihood estimator. The asymptotics of these statistics are elucidated. It is shown that their
asymptotic distributions do not depend on non-Gaussianity of the processes. Because our models include nonlinear stationary
time series models, we can apply the results to stationary GARCH processes. Advantage of the proposed estimator is demonstrated
by a few simulated numerical examples. 相似文献
3.
Consider a sequence of estimators [^(q)] n\hat \theta _n which converges almost surely to θ
0 as the sample size n tends to infinity. Under weak smoothness conditions, we identify the asymptotic limit of the last time [^(q)] n\hat \theta _n is further than ɛ away from θ
0 when ɛ → 0+. These limits lead to the construction of sequentially fixed width confidence regions for which we find analytic approximations.
The smoothness conditions we impose is that [^(q)] n\hat \theta _n is to be close to a Hadamard-differentiable functional of the empirical distribution, an assumption valid for a large class
of widely used statistical estimators. Similar results were derived in Hjort and Fenstad (1992) for the case of Euclidean
parameter spaces; part of the present contribution is to lift these results to situations involving parameter functionals.
The apparatus we develop is also used to derive appropriate limit distributions of other quantities related to the far tail
of an almost surely convergent sequence of estimators, like the number of times the estimator is more than ɛ away from its target. We illustrate our results by giving a new sequential simultaneous confidence set for the cumulative
hazard function based on the Nelson-Aalen estimator and investigate a problem in stochastic programming related to computational
complexity. 相似文献
4.
K VISHNU NAMBOOTHIRI 《Proceedings Mathematical Sciences》2011,121(1):1-18
Consider an irreducible, admissible representation π of GL(2,F) whose restriction to GL(2,F) + breaks up as a sum of two irreducible representations π
+ + π
−. If π = r
θ
, the Weil representation of GL(2,F) attached to a character θ of K
* does not factor through the norm map from K to F, then c ? [^(K*)]\chi\in \widehat{K^*} with (c. q-1)| F * =w K/F(\chi . \theta ^{-1})\vert _{ F^{ * }}=\omega _{ {K/F}} occurs in r
θ
+ if and only if e(qc-1,y0)=e([`(q)]c-1,y0)=1\epsilon(\theta\chi^{-1},\psi_0)=\epsilon(\overline \theta\chi^{-1},\psi_0)=1 and in r
θ
− if and only if both the epsilon factors are − 1. But given a conductor n, can we say precisely how many such χ will appear in π? We calculate the number of such characters at each given conductor n in this work. 相似文献
5.
We consider generalized Morrey type spaces Mp( ·),q( ·),w( ·)( W) {\mathcal{M}^{p\left( \cdot \right),\theta \left( \cdot \right),\omega \left( \cdot \right)}}\left( \Omega \right) with variable exponents p(x), θ(r) and a general function ω(x, r) defining a Morrey type norm. In the case of bounded sets
W ì \mathbbRn \Omega \subset {\mathbb{R}^n} , we prove the boundedness of the Hardy–Littlewood maximal operator and Calderón–Zygmund singular integral operators with
standard kernel. We prove a Sobolev–Adams type embedding theorem Mp( ·),q1( ·),w1( ·)( W) ? Mq( ·),q2( ·),w2( ·)( W) {\mathcal{M}^{p\left( \cdot \right),{\theta_1}\left( \cdot \right),{\omega_1}\left( \cdot \right)}}\left( \Omega \right) \to {\mathcal{M}^{q\left( \cdot \right),{\theta_2}\left( \cdot \right),{\omega_2}\left( \cdot \right)}}\left( \Omega \right) for the potential type operator I
α(·) of variable order. In all the cases, we do not impose any monotonicity type conditions on ω(x, r) with respect to r. Bibliography: 40 titles. 相似文献
6.
Changxing Miao Liutang Xue 《NoDEA : Nonlinear Differential Equations and Applications》2011,18(6):707-735
In this paper we consider the following 2D Boussinesq–Navier–Stokes systems
lll?t u + u ·?u + ?p = - n|D|a u + qe2 ?t q+u·?q = - k|D|b q div u = 0{\begin{array}{lll}\partial_t u + u \cdot \nabla u + \nabla p = - \nu |D|^\alpha u + \theta e_2\\ \quad\quad \partial_t \theta+u\cdot\nabla \theta = - \kappa|D|^\beta \theta \\ \quad\quad\quad\quad\quad{\rm div} u = 0\end{array}} 相似文献
7.
K. V. Solich 《Ukrainian Mathematical Journal》2011,63(6):940-961
We obtain exact-order estimates for the best bilinear approximations of the classes Sp,qW B S_{p,\theta }^\Omega B of periodic functions of many variables in the space L
q
under certain restrictions on the parameters p, q, and θ. 相似文献
8.
Christopher S. Withers Saralees Nadarajah 《Annals of the Institute of Statistical Mathematics》2010,62(6):1113-1142
We obtain the Edgeworth expansion for P(n1/2([^(q)]-q) < x){P(n^{1/2}(\hat{\theta}-\theta) < x)} and its derivatives, and the tilted Edgeworth (or saddlepoint or small sample) expansion for P([^(q)] < x){P(\hat{\theta} < x)} and its derivatives where [^(q)]{\hat{\theta}} is any vector estimate having the standard cumulant expansions in powers of n-1{n^{-1}} . 相似文献
9.
Lasha Ephremidze Gigla Janashia Edem Lagvilava 《Journal of Fourier Analysis and Applications》2011,17(5):976-990
It is proved that if positive definite matrix functions (i.e. matrix spectral densities) S
n
, n=1,2,… , are convergent in the L
1-norm, ||Sn-S||L1? 0\|S_{n}-S\|_{L_{1}}\to 0, and ò02plogdetSn(eiq) dq?ò02plogdetS(eiq) dq\int_{0}^{2\pi}\log \mathop{\mathrm{det}}S_{n}(e^{i\theta})\,d\theta\to\int_{0}^{2\pi}\log \mathop{\mathrm{det}}S(e^{i\theta})\,d\theta, then the corresponding (canonical) spectral factors are convergent in L
2, ||S+n-S+||L2? 0\|S^{+}_{n}-S^{+}\|_{L_{2}}\to 0. The formulated logarithmic condition is easily seen to be necessary for the latter convergence to take place. 相似文献
10.
We extend a result of ?estakov to compare the complex interpolation method [X 0, X 1]θ with Calderón-Lozanovskii’s construction ${{{{X^{1-\theta}_{0}X^{\theta}_{1}}}}}
11.
An error analysis of Runge–Kutta convolution quadrature is presented for a class of non-sectorial operators whose Laplace
transform satisfies, besides the standard assumptions of analyticity in a half-plane Re s > σ
0 and a polynomial bound
\operatornameO(|s|m1){\operatorname{O}(|s|^{\mu_1})} there, the stronger polynomial bound
\operatornameO(sm2){\operatorname{O}(s^{\mu_2})} in convex sectors of the form
|\operatorname*arg s| £ p/2-q{|\operatorname*{arg} s| \leq \pi/2-\theta} for θ > 0. The order of convergence of the Runge–Kutta convolution quadrature is determined by μ
2 and the underlying Runge–Kutta method, but is independent of μ
1. Time domain boundary integral operators for wave propagation problems have Laplace transforms that satisfy bounds of the
above type. Numerical examples from acoustic scattering show that the theory describes accurately the convergence behaviour
of Runge–Kutta convolution quadrature for this class of applications. Our results show in particular that the full classical
order of the Runge–Kutta method is attained away from the scattering boundary. 相似文献
12.
For the least upper bounds of deviations of the de la Vallée-Poussin operators on the classes [^(L)]by \hat{L}_\beta^\psi of rapidly vanishing functions ψ in the metric of the spaces [^(L)]p {\hat{L}_p} , 1 ≤ p ≤ ∞, we establish upper estimates that are exact on some subsets of functions from [^(L)]p {\hat{L}_p} . 相似文献
13.
S. A. Stasyuk 《Ukrainian Mathematical Journal》2011,63(4):638-645
We obtain an exact-order estimate for the best m-term approximation of the classes B¥, qr B_{\infty, \theta }^r of periodic functions of many variables by polynomials in the Haar system in the metric of the space L
q
, 1 < q < ∞. 相似文献
14.
We study the first vanishing time for solutions of the Cauchy–Dirichlet problem for the 2m-order (m ≥ 1) semilinear parabolic equation ${u_t + Lu + a(x) |u|^{q-1}u=0,\,0 < q < 1}
15.
Zhiting Xu 《Monatshefte für Mathematik》2007,57(5):157-171
Some oscillation criteria are established by the averaging technique for the second order neutral delay differential equation
of Emden-Fowler type
(a(t)x¢(t))¢+q1(t)| y(t-s1)|a sgn y(t-s1) +q2(t)| y(t-s2)|b sgn y(t-s2)=0, t 3 t0,(a(t)x'(t))'+q_1(t)| y(t-\sigma_1)|^{\alpha}\,{\rm sgn}\,y(t-\sigma_1) +q_2(t)| y(t-\sigma_2)|^{\beta}\,{\rm sgn}\,y(t-\sigma_2)=0,\quad t \ge t_0,
where x(t) = y(t) + p(t)y(t − τ), τ, σ1 and σ2 are nonnegative constants, α > 0, β > 0, and a, p, q
1,
q2 ? C([t0, ¥), \Bbb R)q_2\in C([t_0, \infty), {\Bbb R})
. The results of this paper extend and improve some known results. In particular, two interesting examples that point out
the importance of our theorems are also included. 相似文献
16.
S. P. Voitenko 《Ukrainian Mathematical Journal》2009,61(9):1404-1416
We obtain exact order estimates for the best M -term trigonometric approximations of the classes Bp,qW B_{p,\theta }^\Omega of periodic functions of many variables in the space L
q
. 相似文献
17.
In this paper, we study the planar Hamiltonian system = J (A(θ)x + ▽f(x, θ)), θ = ω, x ∈ R2 , θ∈ Td , where f is real analytic in x and θ, A(θ) is a 2 × 2 real analytic symmetric matrix, J = (1-1 ) and ω is a Diophantine vector. Under the assumption that the unperturbed system = JA(θ)x, θ = ω is reducible and stable, we obtain a series of criteria for the stability and instability of the equilibrium of the perturbed system. 相似文献
18.
Violeta Petkova 《Archiv der Mathematik》2009,93(4):357-368
We study the spectrum σ(M) of the multipliers M which commute with the translations on weighted spaces ${L_{\omega}^{2}(\mathbb{R})}
19.
Let K be either the rational number field
\Bbb Q{\Bbb Q} or an imaginary quadratic field. We give irrationality results for the number q = ?n=1¥rn/(qn-rl)\theta=\sum_{n=1}^{\infty}{r^n}/(q^n-r^l), where q (∣q∣ > 1) is an integer in K, r∈ K
× (∣r∣ < ∣q∣), and
1 £ l ? \Bbb Z1\le l\in{\Bbb Z} with q
n
≠ r
l (n ≥ 1). 相似文献
20.
E. Stepanov 《Journal of Mathematical Sciences》2010,167(3):406-417
We prove that every real flat chain T of finite mass in a complete separable metric space E is rectifiable when
\mathbbMa (T) < + ¥ {\mathbb{M}^\alpha }(T) < + \infty for some α ∈ [0, 1), where
\mathbbMa (T) {\mathbb{M}^\alpha }(T) is the α-mass of T. Bibliography: 12 titles. 相似文献
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