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1.
In this paper, we establish strong laws for weighted sums of identically distributed negatively associated random variables.
Marcinkiewicz-Zygmund’s strong law of large numbers is extended to weighted sums of negatively associated random variables.
Furthermore, we investigate various limit properties of Cesàro’s and Riesz’s sums of negatively associated random variables.
Some of the results in the i.i.d. setting, such as those in Jajte (Ann. Probab. 31(1), 409–412, 2003), Bai and Cheng (Stat. Probab. Lett. 46, 105–112, 2000), Li et al. (J. Theor. Probab. 8, 49–76, 1995) and Gut (Probab. Theory Relat. Fields 97, 169–178, 1993) are also improved and extended to the negatively associated setting.
相似文献
2.
We discuss the complete convergence of weighted sums for arrays of rowwise negatively dependent random variables (ND r.v.’s)
to linear processes. As an application, we obtain the complete convergence of linear processes based on ND r.v.’s which extends
the result of Li et al. (Stat. Probab. Lett. 14:111–114, 1992), including the results of Baum and Katz (Trans. Am. Math. Soc. 120:108–123, 1965), from the i.i.d. case to a negatively dependent (ND) setting. We complement the results of Ahmed et al. (Stat. Probab. Lett.
58:185–194, 2002) and confirm their conjecture on linear processes in the ND case. 相似文献
3.
Precise Large Deviations for Sums of Negatively Associated Random Variables with Common Dominatedly Varying Tails 总被引:1,自引:0,他引:1
Yue Bao WANG Kai Yong WANG Dong Ya CHENG 《数学学报(英文版)》2006,22(6):1725-1734
In this paper, we obtain results on precise large deviations for non-random and random sums of negatively associated nonnegative random variables with common dominatedly varying tail distribution function. We discover that, under certain conditions, three precise large-deviation prob- abilities with different centering numbers are equivalent to each other. Furthermore, we investigate precise large deviations for sums of negatively associated nonnegative random variables with certain negatively dependent occurrences. The obtained results extend and improve the corresponding results of Ng, Tang, Yan and Yang (J. Appl. Prob., 41, 93-107, 2004). 相似文献
4.
Consider the ensemble of real symmetric Toeplitz matrices whose entries are i.i.d. random variables chosen from a fixed probability
distribution p of mean 0, variance 1, and finite higher moments. Previous work (Bryc et al., Ann. Probab. 34(1):1–38, 2006; Hammond and Miller, J. Theor. Probab. 18(3):537–566, 2005) showed that the spectral measures (the density of normalized eigenvalues) converge almost surely to a universal distribution
almost that of the Gaussian, independent of p. The deficit from the Gaussian distribution is due to obstructions to solutions of Diophantine equations and can be removed
(see Massey et al., J. Theor. Probab. 20(3):637–662, 2007) by making the first row palindromic. In this paper we study the case where there is more than one palindrome in the first
row of real symmetric Toeplitz matrices. Using the method of moments and an analysis of the resulting Diophantine equations,
we show that the spectral measures converge almost surely to a universal distribution. Assuming a conjecture on the resulting
Diophantine sums (which is supported by numerics and some theoretical arguments), we prove that the limiting distribution
has a fatter tail than any previously seen limiting spectral measure. 相似文献
5.
Cedric Boutillier Sevak Mkrtchyan Nicolai Reshetikhin Peter Tingley 《Annales Henri Poincare》2012,13(2):271-296
Random skew plane partitions of large size distributed according to an appropriately scaled Schur process develop limit shapes.
In the present work, we consider the limit of large random skew plane partitions where the inner boundary approaches a piecewise
linear curve with non-lattice slopes, describing the limit shape and the local fluctuations in various regions. This analysis
is fairly similar to that in Okounkov and Reshetikhin (Commun Math Phys 269:571–609, 2007), but we do find some new behavior. For instance, the boundary of the limit shape is now a single smooth (not algebraic)
curve, whereas the boundary in Okounkov and Reshetikhin (Commun Math Phys 269:571–609, 2007) is singular. We also observe the bead process introduced in Boutillier (Ann Probab 37(1):107–142, 2009) appearing in the asymptotics at the top of the limit shape. 相似文献
6.
We investigate precise large deviations for heavy-tailed random sums. We prove a general asymptotic relation in the compound
renewal risk model for consistently varying-tailed distributions. This model was introduced in [Q. Tang, C. Su, T. Jiang,
and J.S. Zang, Large deviation for heavy-tailed random sums in compound renewal model, Stat. Probab. Lett., 52:91–100, 2001] as a more practical risk model. The proof is based on the inequality found in [D. Fuk and S.V. Nagaev,
Probability for sums of independent random variables, Theory Probab. Appl., 16:600–675, 1971]. 相似文献
7.
Yizao Wang 《Extremes》2012,15(2):175-196
We provide a necessary and sufficient condition for the ratio of two jointly α-Fréchet random variables to be regularly varying. This condition is based on the spectral representation of the joint distribution
and is easy to check in practice. Our result motivates the notion of the ratio tail index, which quantifies dependence features that are not characterized by the tail dependence index. As an application, we derive the asymptotic behavior of the quotient correlation coefficient proposed in Zhang (Ann Stat
36(2):1007–1030, 2008) in the dependent case. Our result also serves as an example of a new type of regular variation of products, different from
the ones investigated by Maulik et al (J Appl Probab 39(4):671–699, 2002). 相似文献
8.
In this paper, we study sums of linear random fields defined on the lattice Z
2 with values in a Hilbert space. The rate of convergence of distributions of such sums to the Gaussian law is discussed, and
mild sufficient conditions to obtain an approximation of order n
−p
are presented. This can be considered as a complement of a recent result of [A.N. Nazarova, Logarithmic velocity of convergence
in CLT for stochastic linear processes and fields in a Hilbert space, Fundam. Prikl. Mat., 8:1091–1098, 2002 (in Russian)], where the logarithmic rate of convergence was stated, and as a generalization of the result of [D. Bosq, Erratum
and complements to Berry–Esseen inequality for linear processes in Hilbert spaces, Stat. Probab. Lett., 70:171–174, 2004] for linear processes. 相似文献
9.
Toshiyuki Katsuda 《Queueing Systems》2010,65(3):237-273
Recently Gamarnik and Zeevi (Ann. Appl. Probab. 16:56–90, 2006) and Budhiraja and Lee (Math. Oper. Res. 34:45–56, 2009) established that, under suitable conditions, a sequence of the stationary scaled queue lengths in a generalized Jackson
queueing network converges to the stationary distribution of multidimensional reflected Brownian motion in the heavy-traffic
regime. In this work we study the corresponding problem in multiclass queueing networks (MQNs). 相似文献
10.
In classical extreme value theory probabilities of extreme events are estimated assuming all the components of a random vector
to be in a domain of attraction of an extreme value distribution. In contrast, the conditional extreme value model assumes
a domain of attraction condition on a sub-collection of the components of a multivariate random vector. This model has been
studied in Heffernan and Tawn (JRSS B 66(3):497–546, 2004), Heffernan and Resnick (Ann Appl Probab 17(2):537–571, 2007), and Das and Resnick (2009). In this paper we propose three statistics which act as tools to detect this model in a bivariate set-up. In addition, the
proposed statistics also help to distinguish between two forms of the limit measure that is obtained in the model. 相似文献
11.
Jérôme Dedecker Florence Merlevède Dalibor Volný 《Journal of Theoretical Probability》2007,20(4):971-1004
In this paper we study the central limit theorem and its weak invariance principle for sums of non-adapted stationary sequences,
under different normalizations. Our conditions involve the conditional expectation of the variables with respect to a given
σ-algebra, as done in Gordin (Dokl. Akad. Nauk SSSR 188, 739–741, 1969) and Heyde (Z. Wahrsch. verw. Gebiete 30, 315–320, 1974). These conditions are well adapted to a large variety of examples, including linear processes with dependent innovations
or regular functions of linear processes. 相似文献
12.
In some earlier work, we have considered extensions of Lai’s (Ann. Probab. 2:432–440, 1974) law of the single logarithm for delayed sums to a multi-index setting with the same as well as different expansion rates
in the various dimensions. A further generalization concerns window sizes that are regularly varying with index 1 (on the
line). In the present paper, we establish multi-index versions of the latter as well as for some mixtures of expansion rates.
In order to keep things within reasonable size, we confine ourselves to some special cases for the index set
\mathbbZ+2\mathbb{Z}_{+}^{2}
. 相似文献
13.
This paper explores the joint extreme-value behavior of discontinuous random variables. It is shown that as in the continuous
case, the latter is characterized by the weak limit of the normalized componentwise maxima and the convergence of any compatible
copula. Illustrations are provided and an extension to the case of triangular arrays is considered which sheds new light on
recent work of Coles and Pauli (Stat Probab Lett 54:373–379, 2001) and Mitov and Nadarajah (Extremes 8:357–370, 2005). This leads to considerations on the meaning of the bivariate upper tail dependence coefficient of Joe (Comput Stat Data
Anal 16:279–297, 1993) in the discontinuous case. 相似文献
14.
The polynomial birth–death distribution (abbreviated, PBD) on ℐ={0,1,2,…} or ℐ={0,1,2,…,m} for some finite m introduced in Brown and Xia (Ann. Probab. 29:1373–1403, 2001) is the equilibrium distribution of the birth–death process with birth rates {α
i
} and death rates {β
i
}, where α
i
≥0 and β
i
≥0 are polynomial functions of i∈ℐ. The family includes Poisson, negative binomial, binomial, and hypergeometric distributions. In this paper, we give probabilistic
proofs of various Stein’s factors for the PBD approximation with α
i
=a and β
i
=i+bi(i−1) in terms of the Wasserstein distance. The paper complements the work of Brown and Xia (Ann. Probab. 29:1373–1403, 2001) and generalizes the work of Barbour and Xia (Bernoulli 12:943–954, 2006) where Poisson approximation (b=0) in the Wasserstein distance is investigated. As an application, we establish an upper bound for the Wasserstein distance
between the PBD and Poisson binomial distribution and show that the PBD approximation to the Poisson binomial distribution
is much more precise than the approximation by the Poisson or shifted Poisson distributions.
相似文献
15.
Gabriel Faraud 《Journal of Theoretical Probability》2011,24(1):194-239
We study a model of diffusion in a Brownian potential. This model was first introduced by T. Brox (Ann. Probab. 14:1206–1218,
1986) as a continuous time analogue of random walk in random environment. We estimate the deviations of this process above or
under its typical behavior. Our results rely on different tools such as a representation introduced by Y. Hu, Z. Shi and M. Yor,
Kotani’s lemma, introduced at first by K. Kawazu and H. Tanaka (J. Math. Soc. Jpn. 49:189–211, 1997), and a decomposition of hitting times developed in a recent article by A. Fribergh, N. Gantert and S. Popov (Preprint, 2008). Our results are in agreement with their results in the discrete case. 相似文献
16.
Brown–Resnick processes form a flexible class of stationary max-stable processes based on Gaussian random fields. With regard
to applications, fast and accurate simulation of these processes is an important issue. In fact, Brown–Resnick processes that
are generated by a dissipative flow do not allow for good finite approximations using the definition of the processes. On
large intervals we get either huge approximation errors or very long operating times. Looking for solutions of this problem,
we give different representations of the Brown–Resnick processes—including random shifting and a mixed moving maxima representation—and
derive various kinds of finite approximations that can be used for simulation purposes. Furthermore, error bounds are calculated
in the case of the original process by Brown and Resnick (J Appl Probab 14(4):732–739, 1977). For a one-parametric class of Brown–Resnick processes based on the fractional Brownian motion we perform a simulation study
and compare the results of the different methods concerning their approximation quality. The presented simulation techniques
turn out to provide remarkable improvements. 相似文献
17.
Gaku Sadasue 《Journal of Theoretical Probability》2008,21(3):571-585
Quasi-invariance of infinite product measures is studied when a locally compact second countable group acts on a standard
Borel space. A characterization of l
2-quasi-invariant infinite product measures is given. The group that leaves the measure class invariant is also studied. In
the case where the group acts on itself by translations, our result extends previous ones obtained by Shepp (Ann. Math. Stat.
36:1107–1112, 1965) and by Hora (Math. Z. 206:169–192, 1991; J. Theor. Probab. 5:71–100, 1992) to all connected Lie groups.
相似文献
18.
In this paper, we continue an asymptotic analysis of a stochastic version of the Lotka–Volterra model for predator–prey interactions.
While the fluid approximation and large deviations were shown in Klebaner and Liptser (Ann. Appl. Probab. 11, 1263–1291, 2001) here we establish the diffusion approximation and moderate deviations. 相似文献
19.
Karl Sigman 《Queueing Systems》2012,70(1):37-43
We present an exact simulation algorithm for the stationary distribution of customer delay for FIFO M/G/c queues in which
ρ=λ/μ<c. In Sigman (J. Appl. Probab. 48A:209–216, 2011) an exact simulation algorithm was presented but only under the strong condition that ρ<1 (super stable case). We only assume that the service-time distribution G(x)=P(S≤x), x≥0, with mean 0<E(S)=1/μ<∞, and its corresponding equilibrium distribution $G_{e}(x)=\mu\int_{0}^{x} P(S>y)\,dy$G_{e}(x)=\mu\int_{0}^{x} P(S>y)\,dy are such that samples of them can be simulated. Unlike the methods used in Sigman (J. Appl. Probab. 48A:209–216, 2011) involving coupling from the past, here we use different methods involving discrete-time processes and basic regenerative
simulation, in which, as regeneration points, we use return visits to state 0 of a corresponding random assignment (RA) model
which serves as a sample-path upper bound. 相似文献
20.
Hui He 《Journal of Theoretical Probability》2011,24(3):688-728
Recently, it has been shown that stochastic spatial Lotka–Volterra models, when suitably rescaled, can converge to a super-Brownian
motion. We show that the limit process can be a super-stable process if the kernel of the underlying motion is in the domain
of attraction of a stable law. The corresponding results in the Brownian setting were proved by Cox and Perkins (Ann. Probab.
33(3):904–947, 2005; Ann. Appl. Probab. 18(2):747–812, 2008). As applications of the convergence theorems, some new results on the asymptotics of the voter model started from single
1 at the origin are obtained, which improve the results by Bramson and Griffeath (Z. Wahrsch. Verw. Geb. 53:183–196, 1980). 相似文献