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1.
Let
be a fractional Brownian motion with parameter 0 < H < 1. We are interested in the estimation of this parameter. To achieve this goal, we consider certain functionals of the
second order increments of b
H
(·), using variation technics. Based on an almost-sure convergence theorem for general functionals, we single out particular
functionals that allows to construct certain regression models for the parameter H. We show that this regression based estimator for H is asymptotically unbiased, consistent and that it satisfies a Central Limit Theorem.
相似文献
2.
3.
??In this paper, we study a class of stochastic Volterra equations, which include the stochastic differential equation driven by fractional Brownian motion. By using a maximal inequality due to It\^o (1979), we establish the central limit theorem for stochastic Volterra equation on the continuous path space, with respect to the uniform norm. 相似文献
4.
Philippe Carmona Laure Coutin G. Montseny 《Statistical Inference for Stochastic Processes》2000,3(1-2):161-171
We study a class of processes which have a moving average representation with respect to a fixed driving martingale, and can be represented as a mixture of semi-martingale processes. When the driving martingale is Gaussian we obtain a numerically efficient approximation scheme and a central limit theorem (a typical process in this class is fractional Brownian motion). 相似文献
5.
M. Vaičiulis 《Lithuanian Mathematical Journal》2009,49(2):222-233
In this paper, we introduce an increment ratio statistic (IR
N,m
) based estimator for estimation of the tail index of a heavy-tailed distribution. For i.i.d. observations depending on the
zone of attraction of an α-stable law (0 < α < 2), the IR
N,m
statistic converges to a decreasing function L(α) as both the sample size N and bandwidth parameter m tend to infinity. We obtain a rate of decay of the bias EIR
N,m
−L(α) and mean square error E(IR
N,m
−L(α))2. A central limit theorem (IR
N,m
−EIR
N,m
)⟹ (0,σ2(α)) is also obtained. Monte Carlo simulations show that our tail index estimator has quite good empirical mean square error
and, unlike the Hill estimator, is not so sensitive to a change of bandwidth parameter m.
The research was partially supported by the Lithuanian State Science and Studies Foundation, grant No. T-25/08. 相似文献
6.
We investigate the joint weak convergence (f.d.d. and functional) of the vector-valued process (U
n
(1)
(τ), U
n
(2)
(τ)) for τ ∈ [0, 1], where
and
are normalized partial-sum processes separated by a large lag m, m/n → ∞, and (X
t
, t ∈ ℤ) is a stationary moving-average process with i.i.d. (or martingale-difference) innovations having finite variance. We
consider the cases where (X
t
) is a process with long memory, short memory, or negative memory. We show that, in all these cases, as n → ∞ and m/n → ∞, the bivariate partial-sum process (U
n
(1)
(τ), U
n
(2)
(τ)) tends to a bivariate fractional Brownian motion with independent components. The result is applied to prove the consistency
of certain increment-type statistics in moving-average observations.
This work supported by the joint Lithuania-French research program Gilibert.
__________
Translated from Lietuvos Matematikos Rinkinys, Vol. 45, No. 4, pp. 479–500, October–December, 2005. 相似文献
7.
The main result is that the necessary and sufficient conditions for the central limit theorem for centered, second-order processes given by Giné and Zinn(6) can be obtained without any basic measurability condition. Furthermore we extend some of their results. 相似文献
8.
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
9.
We construct an independent increments Gaussian process associated to a class of multicolor urn models. The construction uses
random variables from the urn model which are different from the random variables for which central limit theorems are available
in the two color case. 相似文献
10.
We prove large deviation principles for the almost everywhere central limit theorem, assuming that the i.i.d. summands have finite moments of all orders. The level 3 rate function is a specific entropy relative to Wiener measure and the level 2 rate the Donsker-Varadhan entropy of the Ornstein-Uhlenbeck process. In particular, the rate functions are independent of the particular distribution of the i.i.d. process under study. We deduce these results from a large deviation theory for Brownian motion via Skorokhod's representation of random walk as Brownian motion evaluated at random times. The results for Brownian motion come from the well-known large deviation theory of the Ornstein-Uhlenbeck process, by a mapping between the two processes. 相似文献
11.
Zheng Yan LIN Wen Sheng WANG Kyo Shin HWANG 《数学学报(英文版)》2006,22(6):1767-1780
In this paper, we obtain functional limit theorems for d-dimensional FBM in HSlder norm via estimating large deviation probabilities for d-dimensional FBM in HSlder norm. 相似文献
12.
Marie-Christine Düker 《Stochastic Processes and their Applications》2018,128(5):1439-1465
Let be a linear process with values in a separable Hilbert space given by for each , where is a bounded, linear normal operator and is a sequence of independent, identically distributed -valued random variables with and . We investigate the central and the functional central limit theorem for when the series of operator norms diverges. Furthermore, we show that the limit process in case of the functional central limit theorem generates an operator self-similar process. 相似文献
13.
SOME CENTRAL LIMIT THEOREMS FOR SUPER BROWNIAN MOTION 总被引:1,自引:0,他引:1
李增沪 《数学物理学报(B辑英文版)》1999,(2)
1IntroductionLimittheoremsconstituteanimportantpartofthebranchingprocesstheory.Itisalwaysinterestingtofindconditionsunderwhichanon-degeneratelimitlawexists.SinceGaltonWatsonprocessesareunstable,peoplehavederivedlimittheoremsforthemthroughdevicessucllasmodifyingfactors,conditioning,immigration,etc.AunifiedtreatmentofthelimittheoryofGallon--WatsonprocessesisgiveninAthreyaandNey(1972).Someoftheabovementionedtechniqueshavealsobeenusedinthemeasure-valuedsettingtogetlimittheoremsforDawson-Watana… 相似文献
14.
Frequency domain statistics are studied in the presence of fractional deterministic and stochastic trends. It is shown how the behaviour of the sample variance–covariance matrix of nonstationary processes can be dominated by components corresponding to a possibly degenerating band around zero frequency. This property is used to establish the limiting distribution of the averaged periodogram matrix, of memory estimates for nonstationary series, and for frequency domain regression estimates under nonstandard conditions. 相似文献
15.
高斯过程函数的中心极限定理与应用 总被引:1,自引:0,他引:1
采用Wiener空间的两个算子以及相关的恒等式,提出了新的方法证明了关于高斯过程函数的中心极限定理,并给出了该中心极限定理的应用实例. 相似文献
16.
S. G. Kobel’kov 《Mathematical Notes》2006,80(3-4):372-379
For a family of real-valued Gaussian processes ξ u (t), t ∈ [0, T], we obtain an exact asymptotics of the probability of crossing a level u as u → ∞ under certain conditions on the variance and correlation. This result is applied to the investigation of excursions of a stationary zero-mean process above a barrier increasing to infinity. 相似文献
17.
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
18.
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
19.
Anatoliy Malyarenko 《Journal of Theoretical Probability》2006,19(2):263-288
We prove a general functional limit theorem for multiparameter fractional Brownian motion. The functional law of the iterated
logarithm, functional Lévy’s modulus of continuity and many other results are its particular cases. Applications to approximation
theory are discussed.
相似文献
20.
We establish a quenched central limit theorem (CLT) for the branching Brownian motion with random immigration in dimension $d\geq4$. The limit is a Gaussian random measure, which is the same as the annealed central limit theorem, but the covariance kernel of the limit is different from that in the annealed sense when d=4. 相似文献