共查询到20条相似文献,搜索用时 15 毫秒
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Ryozo Yokoyama 《Analysis Mathematica》1983,9(1):79-84
Пусть {Xj} - строго стац ионарная последоват ельностьс ?перемешиванием, EXj-Q,E¦-X j¦r<∞ для некоторогоr>2. Положим \(S_n = \mathop \sum \limits_{j = 1}^n X_j \) . Ибрагимов (1962) доказал, что если приn →∞, то 1 $$\mathop {\lim }\limits_{n \to \infty } P\{ S_n /\sigma _n< x\} = (2\pi )^{ - {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \mathop \smallint \limits_{ - \infty }^x e^{{{ - u^2 } \mathord{\left/ {\vphantom {{ - u^2 } 2}} \right. \kern-\nulldelimiterspace} 2}} du.$$ В работе установлено, что при указанных выш е условиях в этой центральной пр едельной теореме имеет место т акже и сходимостьr-ых абсолютных моментов, т.е. если σ n 2 →∞ приn→ ∞, то $$\mathop {\lim }\limits_{n \to \infty } E|S_n /\sigma _n |^r = (2\pi )^{ - {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \mathop \smallint \limits_{ - \infty }^{ + \infty } |u|^r e^{ - u^2 /2} du.$$ Этот результат обобщ ает один более ранний результат автора (1980 г.). 相似文献
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LetΔ_1(x;φ) be the error term of the first Riesz mean of the Rankin-Selberg problem. We study the higher power moments ofΔ_1(x;φ) and derive an asymptotic formula for the 3-rd, 4-th and 5-th power moments by using Ivic's large value arguments and other techniques. 相似文献
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Simon Baker 《Acta Mathematica Hungarica》2014,142(1):95-109
We study the topology of a set naturally arising from the study of β-expansions. After proving several elementary results for this set we study the case when our base is Pisot. In this case we give necessary and sufficient conditions for this set to be finite. This finiteness property will allow us to generalise a theorem due to Schmidt and will provide the motivation for sufficient conditions under which the growth rate and Hausdorff dimension of the set of β-expansions are equal and explicitly calculable. 相似文献
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Using a coupling for the weighted sum of independent random variables and the explicit expression of the transition semigroup
of Ornstein–Uhlenbeck processes driven by compound Poisson processes, we establish the existence of a successful coupling
and the Liouville theorem for general Ornstein–Uhlenbeck processes. Then we present the explicit coupling property of Ornstein–Uhlenbeck
processes directly from the behaviour of the corresponding symbol or characteristic exponent. This approach allows us to derive
gradient estimates for Ornstein–Uhlenbeck processes via the symbol. 相似文献
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We consider the Erlang loss system, characterized by N servers, Poisson arrivals and exponential service times, and allow the arrival rate to be a function of N. We discuss representations and bounds for the rate of convergence to stationarity of the number of customers in the system, and display some bounds for the total variation distance between the time-dependent and stationary distributions. We also pay attention to time-dependent rates. 相似文献
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We consider the problem of reconstructing a planar convex set from noisy observations of its moments. An estimation method based on pointwise recovering of the support function of the set is developed. We study intrinsic accuracy limitations in the shape–from–moments estimation problem by establishing a lower bound on the rate of convergence of the mean squared error. It is shown that the proposed estimator is near–optimal in the sense of the order. An application to tomographic reconstruction is discussed, and it is indicated how the proposed estimation method can be used for recovering edges from noisy Radon data.Mathematics Subject Classification (2000):62C20, 62G20, 94A12 相似文献
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Lothar Heinrich 《Applications of Mathematics》2016,61(4):443-461
First, we derive a representation formula for all cumulant density functions in terms of the non-negative definite kernel function C(x, y) defining an α-determinantal point process (DPP). Assuming absolute integrability of the function C0(x) = C(o, x), we show that a stationary α-DPP with kernel function C0(x) is “strongly” Brillinger-mixing, implying, among others, that its tail-σ-field is trivial. Second, we use this mixing property to prove rates of normal convergence for shot-noise processes and sketch some applications to statistical second-order analysis of α-DPPs. 相似文献
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XI Fubao & ZHAO Liqin Department of Mathematics Beijing Institute of Technology Beijing China School of Mathematical Sciences Beijing Normal University Beijing China 《中国科学A辑(英文版)》2006,49(9):1258-1274
In this paper we consider the stability for diffusion processes with state-dependent switching. We first prove their Feller continuity by the coupling methods. Furthermore, we also prove their strong Feller continuity and their exponential ergodicity under some reasonable conditions. Finally, we append a very brief discussion about the regularity of these processes. 相似文献
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Tom Kempton 《Acta Mathematica Hungarica》2014,142(2):403-419
We construct a Lebesgue measure preserving natural extension of a skew product system related to the random β-transformation K β . This allows us to give a formula for the density of the absolutely continuous invariant probability measure of K β , answering a question of Dajani and de Vries, and also to evaluate some estimates on the typical branching rate of the set of β-expansions of a real number. 相似文献
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《Chaos, solitons, and fractals》2006,27(5):1363-1375
It is proven that generalized coupled higher-order nonlinear Schrödinger equations possess the Painlevé property for two particular choices of parameters, using the Weiss–Tabor–Carnevale method and Kruskal’s simplification. Abundant families of periodic wave solutions are obtained by using the Jacobi elliptic function expansion method with the assistance of symbolic manipulation system, Maple. It is also shown that these solutions exactly degenerate to bright soliton, dark soliton and mixed dark and bright soliton solutions with physical interests. 相似文献
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The diffusion process in a region ${G \subset \mathbb R^2}$ governed by the operator ${\tilde L^\varepsilon = \frac{\,1}{\,2}\, u_{xx} + \frac1 {2\varepsilon}\, u_{zz}}$ inside the region and undergoing instantaneous co-normal reflection at the boundary is considered. We show that the slow component of this process converges to a diffusion process on a certain graph corresponding to the problem. This allows to find the main term of the asymptotics for the solution of the corresponding Neumann problem in G. The operator ${\tilde L^\varepsilon}$ is, up to the factor ε ? 1, the result of small perturbation of the operator ${\frac{\,1}{\,2}\, u_{zz}}$ . Our approach works for other operators (diffusion processes) in any dimension if the process corresponding to the non-perturbed operator has a first integral, and the ε-process is non-degenerate on non-singular level sets of this first integral. 相似文献
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Nicolas Privault 《Comptes Rendus Mathematique》2013,351(9-10):397-400
We propose a formula for the computation of the moments of all orders of Itô and Skorohod stochastic integrals with respect to Brownian motion, based on cumulant operators defined by the Malliavin calculus. Some characterizations of Gaussian distributions for stochastic integrals are recovered as a consequence. 相似文献
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L. Maria Abatangelo 《Journal of Geometry》1985,25(1):19-29
This paper contains some general results about the automorphism group H of PG(3,q) leaving a -derived spread F invariant. The main result asserts that H contains a cyclic subgroups M*, whose order divides (q+1)/2. In particular, H is not trivial. In terms of translation planes this means that the translation complement of any -derived plane always admits some collineations which are not dilatations.Research partially supported by M.P.I. (Research project Strutture Geometriche Combinatorie e loro Applicazioni). 相似文献
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WANG Bin XIANG Kainan & YANG Xiangqun Department of Mathematics Hunan Normal University Changsha China 《中国科学A辑(英文版)》2006,49(10):1315-1326
A measure-valued diffusion process describing how the measures evolve under flows or "imaginary" flows on Rd is constructed in this paper. The interest of the process is that on the one hand, it can be viewed as a measure-valued flow; on the other hand, the general stochastic flows of measurable maps or kernels do not cover it. 相似文献
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