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1.
We consider the long-range dependent cumulative traffic generated by the superposition of constant rate fluid sources having exponentially distributed intra start times and Pareto distributed durations with finite mean and infinite variance. We prove a sample path moderate deviation principle when the session intensity is increased and the processes are centered and scaled appropriately. The governing rate function is known from large deviation principles for the tail probabilities of fractional Brownian motion. We derive logarithmic tail asymptotics for associated queue length processes when the traffic loads an infinite buffer with constant service rate. The moderate deviation approximation of steady-state queue length tail probabilities is compared to those obtained by computer simulations. 相似文献
2.
This paper studies large and moderate deviation properties of a realized volatility statistic of high frequency financial data. We establish a large deviation principle for the realized volatility when the number of high frequency observations in a fixed time interval increases to infinity. Our large deviation result can be used to evaluate tail probabilities of the realized volatility. We also derive a moderate deviation rate function for a standardized realized volatility statistic. The moderate deviation result is useful for assessing the validity of normal approximations based on the central limit theorem. In particular, it clarifies that there exists a trade-off between the accuracy of the normal approximations and the path regularity of an underlying volatility process. Our large and moderate deviation results complement the existing asymptotic theory on high frequency data. In addition, the paper contributes to the literature of large deviation theory in that the theory is extended to a high frequency data environment. 相似文献
3.
We derive the upper‐tail moderate deviations for the length of a longest increasing subsequence in a random permutation. This concerns the regime between the upper‐tail large‐deviation regime and the central limit regime. Our proof uses a formula to describe the relevant probabilities in terms of the solution of the rank 2 Riemann‐Hilbert problem (RHP); this formula was invented by Baik, Deift, and Johansson [3] to find the central limit asymptotics of the same quantities. In contrast to the work of these authors, who apply a third‐order (nonstandard) steepest‐descent approximation at an inflection point of the transition matrix elements of the RHP, our approach is based on a (more classical) second‐order (Gaussian) saddle point approximation at the stationary points of the transition function matrix elements. © 2001 John Wiley & Sons, Inc. 相似文献
4.
本文在比较一般的条件下得到了平稳NA序列的中偏差下界估计,进而得到平稳NA序列的中偏差原理。 相似文献
5.
Timo Seppäläinen 《Probability Theory and Related Fields》1998,112(2):221-244
We prove a large deviation principle with explicit rate functions for the length of the longest increasing sequence among
Poisson points on the plane. The rate function for lower tail deviations is derived from a 1977 result of Logan and Shepp
about Young diagrams of random permutations. For the upper tail we use a coupling with Hammersley's particle process and convex-analytic
techniques. Along the way we obtain the rate function for the lower tail of a tagged particle in a totally asymmetric Hammersley's
process.
Received: 22 July 1997 / Revised version: 23 March 1998 相似文献
6.
在某种正则条件下,对Bayes估计尾概率收敛速度问题进行了讨论。利用似然理论方法得到了Bayes估计的中偏差下界,从而改善了Bahadur型的收敛结果。 相似文献
7.
本文研究了带小随机扰动的中偏差原理.运用收缩原理和指数逼近方法,Freidlin-Wentzell定理给出了Xε的大偏差原理,从而得到了Xε的中偏差原理. 相似文献
8.
Fuqing Gao 《随机分析与应用》2016,34(2):258-277
In this article, we consider asymptotic behaviors for functionals of dynamical systems with small random perturbations. First, we present a deviation inequality for Gaussian approximation of dynamical systems with small random perturbations under Hölder norms and establish the moderate deviation principle and the central limit theorem for the dynamical systems by the deviation inequality. Then, applying these results to forward-backward stochastic differential equations and diffusions in small time intervals, combining the delta method in large deviations, we give a moderate deviation principle for solutions of forward-backward stochastic differential equations with small random perturbations, and obtain the central limit theorem, the moderate deviation principle and the iterated logarithm law for functionals of diffusions in small time intervals. 相似文献
9.
In this note we provide a large deviation principle for Poisson shot noise processes under heavy tail semi-exponential conditions on the total shot per arrival. As in the light tail case, our result shows an insensitivity property of the model. 相似文献
10.
11.
ZHANG Mei Department of Mathematics Beijing Normal University Beijing China Department of Mathematics The Central University of Finance Economics Beijing China 《中国科学A辑(英文版)》2004,47(3):440-452
We prove a moderate deviation principle for a super-Brownian motion with im-migration of all dimensions, and consequently fill the gap between the central limit theoremand large deviation principle. 相似文献
12.
Yu Miao 《Acta Appl Math》2010,110(3):1077-1085
In the present paper, the form of iterated limits of the moderate deviation principle for dependent variables is considered
and as an application, the moderate deviation principle of m-dependent random variables is obtained. 相似文献
13.
We establish a moderate deviation principle for processes with independent increments under certain growth conditions for the characteristics of the process. Using this moderate deviation principle, we give a new proof of Strassen’s functional law of the iterated logarithm. In particular, we show that any square-integrable Lévy process satisfies Strassen’s law. 相似文献
14.
Kurt Majewski 《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(4):233-257
By proving the continuity of multi-dimensional Skorokhod maps in a quasi-linearly discounted uniform norm on the doubly infinite time interval R, and strengthening know sample path large deviation principles for fractional Brownian motion to this topology, we obtain large deviation principles for the image of multi-dimensional fractional Brownian motions under Skorokhod maps as an immediate consequence of the contraction principle. As an application, we explicitly calculate large deviation decay rates for steady-state tail probabilities of certain queueing systems in multi-dimensional heavy traffic models driven by fractional Brownian motions. 相似文献
15.
We investigate the moderate deviations from the hydrodynamic limit of the empirical density ofparticles and obtain a moderate deviation principle for a symmetric exclusion process. 相似文献
16.
We establish asymptotic upper and lower bounds on the asymptotic decay rate of per-session queue length tail distributions
for a multiple-queue system where a single constant rate server services the queues using the generalized processor sharing
(GPS) scheduling discipline. In the special case where there are only two queues, the upper and lower bounds match, yielding
the optimal bound proved in [15]. The dynamics of bandwidth sharing of a multiple-queue GPS system is captured using the notion
of partial feasible sets, and the bounds are obtained using the sample-path large deviation principle. The results have implications
in call admission control for high-speed communication networks.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
17.
In this paper, we obtain sample path and scalar large deviation principles for the product of sums of positive random variables. We study the case when the positive random variables are independent and identically distributed and bounded away from zero or the left tail decays to zero sufficiently fast. The explicit formula for the rate function of a scalar large deviation principle is given in the case when random variables are exponentially distributed. 相似文献
18.
In this paper, a theorem on the moderate deviation principle for random arrays under m-dependence with unbounded m is established. This partially extends the results of Chen (Stat. Probab. Lett. 35:123–134, 1997). As an application, the moderate deviation principle for the truncation estimator of the variance in the analysis of time
series is obtained.
相似文献
19.
本文考虑无穷维自回归过程经验协方差函数的中偏差原理,仅对自回归过程的随机扰动项做了高斯可积性的假设,这个条件比[4]中的对数Sobolev不等式要弱很多.主要利用了m-相依随机变量的中偏差结果和Ellis-Grtner定理,推广了[6]的结果. 相似文献
20.
《Insurance: Mathematics and Economics》2012,50(3):345-352
We study asymptotic behavior of the empirical conditional value-at-risk (CVaR). In particular, the Berry–Essen bound, the law of iterated logarithm, the moderate deviation principle and the large deviation principle for the empirical CVaR are obtained. We also give some numerical examples. 相似文献