共查询到20条相似文献,搜索用时 15 毫秒
1.
We prove an invariance principle under self-normalization by blocks for linear processes with summable filters and i.i.d.
innovations in the domain of attraction of the normal distribution. 相似文献
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Let $ {{\left( {{\xi_n}} \right)}_{{n\in \mathbb{Z}}}} $ be a stationary sequence of real random variables with E ξ 0 = 0 and infinite variance. Furthermore, assume that $ {{\left( {{c_n}} \right)}_{{n\in \mathbb{Z}}}} $ is a sequence of real numbers and $ {X_n}=\sum {_{{j\in \mathbb{Z}}}{c_j}{\xi_{n-j }}} $ is a moving average processes driven by $ {{\left( {{\xi_n}} \right)}_{{n\in \mathbb{Z}}}} $ . By using a decomposition of the moving average processes, a central limit theorem for the partial sums $ \sum\nolimits_{k=1}^n {{X_k}} $ is established. As applications, we obtain some central limit theorems for stationary dependent sequences $ {{\left( {{\xi_n}} \right)}_{{n\in \mathbb{Z}}}} $ , such as associated sequence, martingale difference, and so on. 相似文献
7.
A univariate Hawkes process is a simple point process that is self-exciting and has a clustering effect. The intensity of this point process is given by the sum of a baseline intensity and another term that depends on the entire past history of the point process. Hawkes processes have wide applications in finance, neuroscience, social networks, criminology, seismology, and many other fields. In this paper, we prove a functional central limit theorem for stationary Hawkes processes in the asymptotic regime where the baseline intensity is large. The limit is a non-Markovian Gaussian process with dependent increments. We use the resulting approximation to study an infinite-server queue with high-volume Hawkes traffic. We show that the queue length process can be approximated by a Gaussian process, for which we compute explicitly the covariance function and the steady-state distribution. We also extend our results to multivariate stationary Hawkes processes and establish limit theorems for infinite-server queues with multivariate Hawkes traffic. 相似文献
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Karl Lindberger 《Probability Theory and Related Fields》1978,44(1):47-56
Summary Consider a cumulative regenerative process with increments between regeneration points being i.i.d. r.v.'s. Let the d.f. of those increments belong to the domain of attraction of a stable distribution with exponent less than two. A functional limit theorem in the Skorohod M
1-topology is proved for this process. The M
1-topology is more useful than the J
1-topology in this case, because it allows the cumulative process to be continuous.The second part of the paper concerns a stopping time process, (t)--inf(s>0:w(s)>tg(s)), where w(t) is a process with positive drift for which a functional limit theorem holds and g(t)=t
p
L(t) with 0p<1 and L(t) varying slowly at infinity. Weak convergence for the process (t) is proved under certain conditions in the J
1- and M
1-topologies. 相似文献
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陈佳 《高校应用数学学报(A辑)》2007,22(3):316-322
对于均值为零的平稳相伴随机变量序列,首先证明了在L(n)=EX_1~2 2 sum from n to j=2 Cov(X_1,X_j)是一个缓变函数的条件下的泛函型几乎处处中心极限定理.另外还给出了正则化部分和函数的对数平均几乎处处收敛性. 相似文献
12.
In this paper, we establish functional convergence theorems for second order quadratic variations of Gaussian processes which admit a singularity function. First, we prove a functional almost sure convergence theorem, and a functional central limit theorem, for the process of second order quadratic variations, and we illustrate these results with the example of the fractional Brownian sheet (FBS). Second, we do the same study for the process of localized second order quadratic variations, and we apply the results to the multifractional Brownian motion (MBM). 相似文献
13.
I. K. Matsak 《Ukrainian Mathematical Journal》2008,60(12):1955-1967
We investigate conditions for the weak convergence of the maximum of sums of independent random processes in the space L
p
and present several applications to the asymptotic analysis of certain ω
2-type statistics.
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 12, pp. 1664–1674, December, 2008. 相似文献
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E. Permiakova 《Lithuanian Mathematical Journal》2007,47(1):67-77
In this paper, we prove a criterion of convergence in distribution in the Skorokhod space. We apply this criterion to some
special Levy processes and obtain almost-sure versions of limit theorems for these processes.
Published in Lietuvos Matematikos Rinkinys, Vol. 47, No. 1, pp. 81–92, January–March, 2007. 相似文献
16.
Miklós Csörg? Yuliya V. Martsynyuk 《Stochastic Processes and their Applications》2011,121(12):2925-2953
Based on an R2-valued random sample {(yi,xi),1≤i≤n} on the simple linear regression model yi=xiβ+α+εi with unknown error variables εi, least squares processes (LSPs) are introduced in D[0,1] for the unknown slope β and intercept α, as well as for the unknown β when α=0. These LSPs contain, in both cases, the classical least squares estimators (LSEs) for these parameters. It is assumed throughout that {(x,ε),(xi,εi),i≥1} are i.i.d. random vectors with independent components x and ε that both belong to the domain of attraction of the normal law, possibly both with infinite variances. Functional central limit theorems (FCLTs) are established for self-normalized type versions of the vector of the introduced LSPs for (β,α), as well as for their various marginal counterparts for each of the LSPs alone, respectively via uniform Euclidean norm and sup–norm approximations in probability. As consequences of the obtained FCLTs, joint and marginal central limit theorems (CLTs) are also discussed for Studentized and self-normalized type LSEs for the slope and intercept. Our FCLTs and CLTs provide a source for completely data-based asymptotic confidence intervals for β and α. 相似文献
17.
Concentration properties and an asymptotic behaviour of distributions of normalized and self-normalized sums are studied in
the randomized model where the observation times are selected from prescribed consecutive integer intervals.
Research supported in part by NSF Gr. No. 0405587 相似文献
18.
A. F. Ronzhin 《Mathematical Notes》1986,40(5):886-893
19.
《Stochastic Processes and their Applications》2005,115(10):1658-1676
For a strongly subcritical branching process in random environment the non-extinction probability at generation n decays at the same exponential rate as the expected generation size and given non-extinction at n the conditional distribution of has a weak limit. Here we prove conditional functional limit theorems for the generation size process as well as for the random environment. We show that given the population survives up to generation n the environmental sequence still evolves in an i.i.d. fashion and that the conditioned generation size process converges in distribution to a positive recurrent Markov chain. 相似文献
20.
A. I. Karoblis 《Journal of Mathematical Sciences》1987,38(5):2279-2287
Let pn(x) and qn(x) be the densities of the n-fold convolutions of the distributions F and G, respectively. One proves estimates for
, expressed in terms of moment characteristics of F — G, under certain restrictions on the densities of F and G. Similar problems are solved for two lattice distributions and for a lattice and a continuous distribution.Translated from Veroyatnostnye Raspredeleniya i Matematicheskaya Statistika, pp. 193–212, 1986. 相似文献