共查询到20条相似文献,搜索用时 15 毫秒
1.
We study several properties of the sub-fractional Brownian motion (fBm) introduced by Bojdecki et al. related to those of the fBm. This process is a self-similar Gaussian process depending on a parameter H ∈ (0, 2) with non stationary increments and is a generalization of the Brownian motion (Bm). The strong variation of the indefinite stochastic integral with respect to sub-fBm is also discussed. 相似文献
2.
Let {Sn, n ≥ 1} be partial sums of independent identically distributed random variables. The almost sure version of CLT is generalized on the case of randomly indexed sums {SNn, n ≥ 1}, where {Nn, n ≥ 1} is a sequence of positive integer‐valued random variables independent of {Sn, n ≥ 1}. The affects of nonrandom centering and norming are considered too (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
3.
Nguyen Tien Dung 《随机分析与应用》2019,37(1):74-89
In this paper, we consider a general class of functionals of stochastic differential equations driven by fractional Brownian motion. For this class, we obtain Gaussian estimates for the density and a quantitative central limit theorem. The main tools of the paper are the techniques of Malliavin calculus. 相似文献
4.
We prove the Malliavin regularity of the solution of a stochastic differential equation driven by a fractional Brownian motion of Hurst parameter H>0.5. The result is based on the Fréchet differentiability with respect to the input function for deterministic differential equations driven by Hölder continuous functions. It is also shown that the law of the solution has a density with respect to the Lebesgue measure, under a suitable nondegeneracy condition. 相似文献
5.
Let be a fractional Brownian motion with Hurst index . Inspired by pathwise integrals and Wick product, in this paper, we consider the forward and symmetric Wick-Itô integrals with respect to BH as follows: in probability, where ◊ denotes the Wick product. We show that the two integrals coincide with divergence-type integral of BH for all . 相似文献
6.
Central limit theorem and almost sure central limit theorem for the product of some partial sums 总被引:1,自引:0,他引:1
Miao Yu 《Proceedings Mathematical Sciences》2008,118(2):289-294
In this paper, we give the central limit theorem and almost sure central limit theorem for products of some partial sums of
independent identically distributed random variables. 相似文献
7.
M. A. Vronskii 《Mathematical Notes》2000,68(4):444-451
In this paper, for the partial sumsS
n
of a stationary associated random process it is proved that the logarithmic averages
converge almost surely. The asymptotic normality of the normalized difference between the logarithmic averages and their
limiting value is established.
Translated fromMatematicheskie Zametki, Vol. 68, No. 4, pp. 513–522, October, 2000. 相似文献
8.
Patrick Cheridito David Nualart 《Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques》2005,41(6):1049-1081
We define a stochastic integral with respect to fractional Brownian motion BH with Hurst parameter that extends the divergence integral from Malliavin calculus. For this extended divergence integral we prove a Fubini theorem and establish versions of the formulas of Itô and Tanaka that hold for all . Then we use the extended divergence integral to show that for every and all , the Russo–Vallois symmetric integral exists and is equal to , where G′=g, while for , does not exist. 相似文献
9.
10.
Let M n denote the partial maximum of a strictly stationary sequence (X n ). Suppose that some of the random variables of (X n ) can be observed and let [(M)tilde]ntilde M_n stand for the maximum of observed random variables from the set {X 1, ..., X n }. In this paper, the almost sure limit theorems related to random vector ([(M)tilde]ntilde M_n , M n ) are considered in terms of i.i.d. case. The related results are also extended to weakly dependent stationary Gaussian sequence as its covariance function satisfies some regular conditions. 相似文献
11.
We prove the almost sure central limit theorems for the maxima of partial sums of r.v.’s under a general condition of dependence due to Doukhan and Louhichi. We will separately consider the centered sequences and the sequences with positive expected values. 相似文献
12.
This paper deals with the problems of consistency and strong consistency of the maximum likelihood estimators of the mean and variance of the drift fractional Brownian motions observed at discrete time instants. Both the central limit theorem and the Berry-Ess′een bounds for these estimators are obtained by using the Stein’s method via Malliavin calculus. 相似文献
13.
Hong Yan Sun 《数学学报(英文版)》2014,30(1):69-78
We establish a central limit theorem for a branching Brownian motion with random immigration under the annealed law,where the immigration is determined by another branching Brownian motion.The limit is a Gaussian random measure and the normalization is t3/4for d=3 and t1/2for d≥4,where in the critical dimension d=4 both the immigration and the branching Brownian motion itself make contributions to the covariance of the limit. 相似文献
14.
In this article, first, we prove some properties of the sub-fractional Brownian motion introduced by Bojdecki et al. [Statist. Probab. Lett. 69(2004):405–419]. Second, we prove the continuity in law, with respect to small perturbations of the Hurst index, in some anisotropic Besov spaces, of some continuous additive functionals of the sub-fractional Brownian motion. We prove that our result can be obtained easily, by using the decomposition in law of the sub-fractional Brownian motion given by Bardina and Bascompte [Collect. Math. 61(2010):191–204] and Ruiz de Chavez and Tudor [Math. Rep. 11(2009):67–74], without using the result of Wu and Xiao [Stoch. Proc. Appl. 119(2009):1823–1844] by connecting the sub-fractional Brownian motion to its stationary Gaussian process through Lamperti’s transform. This decomposition in law leads to a better understanding and simple proof of our result. 相似文献
15.
An almost sure central limit theorem for self-normalized products of sums of i.i.d. random variables
Let X,X1,X2,… be a sequence of independent and identically distributed positive random variables with EX=μ>0. In this paper we show that the almost sure central limit theorem for self-normalized products of sums holds only under the assumptions that X belongs to the domain of attraction of the normal law. 相似文献
16.
Ciprian A. Tudor Nakahiro Yoshida 《Stochastic Processes and their Applications》2019,129(9):3499-3526
We develop the asymptotic expansion theory for vector-valued sequences of random variables in terms of the convergence of the Stein–Malliavin matrix associated with the sequence . Our approach combines the classical Fourier approach and the recent Stein–Malliavin theory. We find the second order term of the asymptotic expansion of the density of and we illustrate our results by several examples. 相似文献
17.
Yong Zhang Xiao-Yun Yang Zhi-Shan Dong 《Journal of Mathematical Analysis and Applications》2009,355(2):708-41
Let be a strictly stationary positively or negatively associated sequence of positive random variables with EX1=μ>0, and VarX1=σ2<∞. Denote , and γ=σ/μ the coefficient of variation. Under suitable conditions, we show that
18.
Zhichao Weng 《Journal of Mathematical Analysis and Applications》2010,367(1):242-248
In this paper, we prove the almost sure limit theorem of the maxima for a kind of strongly dependent stationary Gaussian vector sequences. 相似文献
19.
Survey on normal distributions,central limit theorem,Brownian motion and the related stochastic calculus under sublinear expectations 总被引:1,自引:0,他引:1
ShiGe Peng 《中国科学A辑(英文版)》2009,52(7):1391-1411
This is a survey on normal distributions and the related central limit theorem under sublinear expectation. We also present Brownian motion under sublinear expectations and the related stochastic calculus of Itô’s type. The results provide new and robust tools for the problem of probability model uncertainty arising in financial risk, statistics and other industrial problems. 相似文献
20.
设Xn, n≥1是独立同分布正的随机变量序列, E(X1)=u >0, Var(X1)=σ2, E|X1|3<∞, 记Sn==∑Nk=1Xk, 变异系数γ=σ/u.g是满足一定条件的无界可测函数, 证明了
limN→∞1/logN∑Nn=11/n g((∏nk=1Sk/n!un )1/γ√n )=∫∞0g(x)dF(x),a.s.,
其中 F(•) 是随机变量e√2ξ 的分布函数, ξ 是服从标准正态分布的随机变量. 相似文献