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1.
The problem of asymptotically efficient estimation of the density of invariant measure of a diffusion process is considered.
The efficient estimator is defined with the help of the minimax lower bound on the risk of all estimators. We show that the
local–time and kernel–type estimators are asymptotically efficient for the loss functions with polynomial majorants. The asymptotic
behavior of a wide class of unbiased estimators with the same limit variances is also discussed.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
2.
U. Goginava 《Acta Mathematica Hungarica》2001,93(1-2):59-70
We study the uniform convergence of Walsh-Fourier series of functions on the generalized Wiener class BV (p(n)↑∞) This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
3.
In this paper, we discuss the uniform convergences of Kergin interpolation and its derivatives for smooth functions defined on the disk. We also consider its application to the classical univariate interpolation. 相似文献
4.
Consider a regular diffusion process X with finite speed measure m. Denote the normalized speed measure by μ. We prove that the uniform law of large numbers
holds if the class
has an envelope function that is μ-integrable, or if
is bounded in L
p(μ) for some p>1. In contrast with uniform laws of large numbers for i.i.d. random variables, we do not need conditions on the ‘size’ of
the class
in terms of bracketing or covering numbers. The result is a consequence of a number of asymptotic properties of diffusion
local time that we derive. We apply our abstract results to improve consistency results for the local time estimator (LTE)
and to prove consistency for a class of simple M-estimators.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
5.
PrakasaRao在文献[1]中提出一类密度估计fn(x),我们得到当x固定时fn(x)-f(x)的a.s.收敛速度及fn(x)正态逼近的Berry-Esseen界,同时,给出supx|fn(x)-f(x)|的一致收敛速度 相似文献
6.
We construct time inhomogeneous diffusion processes on a space-time domain D. For each t, the t-section D
t
of D is assumed to be an image of a fixed domain D
0 by a homeomorphic map. After constructing a diffusion process on a fixed domain D
0 by means of the general theory of time dependent Dirichlet forms, transformations by a multiplicative functional and a homeomorphic map are used to get the desired processes. In the case of reflecting difusion process on D, we also give Skorohod type representations of the process by means of the local time on the boundary of D. 相似文献
7.
In a previous work we proposed a kernel method for estimating the value of a state‐dependent diffusion coefficient σ(x) from
discrete time observations. We propose an estimator of the value σ(x), based on the squared length of the transitions where
a crossing past the level x takes place and we investigate its limit properties. Using the Poisson equation and other limit
theorems for discrete martingales, we prove consistency and asymptotic mixed normality of this estimator.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
8.
Based on T. Tao’s celebrated result on the norm convergence of multiple ergodic averages for commuting transformations, we find that there is a subsequence which converges almost everywhere. Meanwhile, we obtain the ergodic behaviour of diagonal measures, which indicates the time average equals the space average. According to the classification of transformations, we also give several different results. Additionally, on the torus Td with special rotation, we prove the pointwise convergence in Td, and get a result for ergodic behaviour. 相似文献
9.
10.
Jonathan M. Borwein Jon D. Vanderwerff 《Transactions of the American Mathematical Society》1996,348(4):1617-1631
We examine when a sequence of lsc convex functions on a Banach space converges uniformly on bounded sets (resp. compact sets) provided it converges Attouch-Wets (resp. Painlevé-Kuratowski). We also obtain related results for pointwise convergence and uniform convergence on weakly compact sets. Some known results concerning the convergence of sequences of linear functionals are shown to also hold for lsc convex functions. For example, a sequence of lsc convex functions converges uniformly on bounded sets to a continuous affine function provided that the convergence is uniform on weakly compact sets and the space does not contain an isomorphic copy of .
11.
Seong-A Shim 《Journal of Differential Equations》2002,185(1):281-305
Uniform boundedness and convergence of global solutions are proved for cross-diffusion systems in population dynamics. Gagliardo-Nirenberg type inequalities are used in the estimates of solutions in order to establish W21-bounds uniform in time. In each step of estimates the contribution of the diffusion coefficients are emphasized, and it is concluded that the uniform bound remains independent of the growth of the diffusion coefficient in the system. Hence convergence of solutions are established for systems with large diffusion coefficients. 相似文献
12.
A sequential asymptotically efficient procedure is constructed for estimating the drift coefficient at a given state point
in ergodic diffusion processes. Sequential kernel estimators are used. The optimal convergence rate with the sharp constant
is given for a local minimax risk. 相似文献
13.
14.
设X为p维随机向量,对于未知的投影方向θo(‖θo‖=1),本文利用θo的估计与核密度估计相结合的方法给出了θ^T0X的密度(方向密度)的核型密度估计,获得了此估计的逐点渐近正态性,逐点精确强收敛率,一致精确强收敛率以及均方误差收敛率,所得结果与最优性与已知方向上的核密度估计完全一致。作为例子,对θo为X协方差阵的最大特征值所对应的特征方向,我们给出了θo的满足条件的估计极其方向密度估计。 相似文献
15.
本文构造了竞争风险场合分布函数的乘积极限(PL)型估计,运用经验过程的强逼近理论及Toylor展开方法,给出了PL型估计在全直线上的强一致收敛速度及其充分必要条件。 相似文献
16.
函数列的一致收敛性与所讨论的区间有关.在区间的子区间或不同的区间上,函数列的一致收敛性表现如何呢?通过几个命题和几个实例,并利用几何画板可以帮助我们辨别函数列在不同区间上的一致收敛性. 相似文献
17.
18.
George Kvernadze 《Journal of Approximation Theory》2002,117(2):207-228
Necessary and sufficient conditions which imply the uniform convergence of the Fourier–Jacobi series of a continuous function are obtained under an assumption that the Fourier–Jacobi series is convergent at the end points of the segment of orthogonality [−1,1]. The conditions are in terms of the modulus of continuity, Λ-variation, and the modulus of variation of a function. 相似文献
19.
设 { ( Xi,Yi) ,i≥ 1 }是独立同分布二维随机向量列 ,其共同分布函数为 F.设 F属于 G的吸引场 ,本文假定边缘分布满足 Von-Mises条件 ,主要考虑二维极大值向量 Mn 密度收敛局部一致成立的问题 .本文将 Resnick[3 ]的结果推广到了二维情形 相似文献