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1.
In this paper, we study asymptotic properties (large deviations and functional central limit theorem) of generalized record
processes built on a triangular array of continuous and exchangeable random variables. As an application of these results,
the links with the Kendall's rank correlation statistic are studied and testing exchangeability is discussed.
AMS 2000 Subject Classification Primary—60F10
Secondary—60F17, 62G10 相似文献
2.
If suitably normalized maxima of an i.i.d. sample converge in distribution, the limiting distribution is known to be max-infinitely
divisible and the common distribution of the sample is said to belong to its domain of attraction. We prove the existence
of max-universal distributions belonging to the domain of attraction of every max-infinitely divisible law. The proof follows
in the spirit of corresponding results for normalized sums of i.i.d. random variables originated by Doeblin and shows that
necessarily the sampling size has to be rapidly increasing. Restricting the growth rate of the sampling size, we prove that
one necessarily deals with max-semistable distributions and their domains of attraction.
2000 Mathematics subject classification Primary—60G70
Secondary—60E99, 60F05 相似文献
3.
George McNinch 《Transformation Groups》2007,12(1):127-135
Let G be a connected and reductive group over the algebraically closed field K. J-P. Serre has introduced the notion of a
G-completely reducible subgroup H ⊂ G. In this paper, we give a notion of G-complete reducibility—G-cr for short—for Lie subalgebras
of Lie(G), and we show that if the closed subgroup H ⊂ G is G-cr, then Lie(H) is G-cr as well. 相似文献
4.
We consider the mean uniform (mixed) norms for a sequence of Gaussian random functions. For a wide class of Gaussian processes
and fields the
-asymptotic for mixed norms is found whenever the volume of the index set is of order
and tends to infinity, for example,
-length time interval for random processes. Some numerical examples demonstrate the rate of convergence for the obtained asymptotic.
The developed technique can be applied to analysis of various linear approximation methods. As an application we consider
the rate of approximation by trigonometrical polynomials in the mean uniform norm.
AMS 2000 Subject Classification Primary—60G70, 60G15; Secondary—60F25 相似文献
5.
We derive asymptotic expansions for tails of infinite weighted convolutions of some heavy-tailed distributions. Applications
are given to tail expansion of the marginal distribution of ARMA processes, randomly stopped sums, as well as limiting waiting
time distribution.
AMS 2000 Subject Classifications. Primary—62E99, Secondary—41A60, 44A35, 60G50, 60K25 相似文献
6.
Suppose the upper records
from a sequence of i.i.d. random variables is in the domain of attraction of a normal distribution. Consider the D(0,1]-valued process {Zn(·)} constructed by usual interpolation of the partial sums of the records. We prove that under some mild conditions, {Zn} converges to a limiting Gaussian process in D(0,1]. As a consequence, the partial sums of records is asymptotically normal.
AMS 2000 Subject Classification Primary—60F17
Secondary—60G70 相似文献
7.
The method of so-called constrained stochastic simulation is introduced. This method specifies how to efficiently generate
time series around some specific event in a normal process. All events which can be expressed by means of a linear condition
(constraint) can be dealt with. Two examples are given in the paper: the generation of stochastic time series around local
maxima and the generation of stochastic time series around a combination of a local minimum and maximum with a specified time
separation. The constrained time series turn out to be a combination of the original process and several correction terms
which includes the autocorrelation function and its time derivatives. For the application concerning local maxima it is shown
that the presented method is in line with properties of a normal process near a local maximum as found in literature. The
method can e.g. be applied to generate wind gusts in order to assess the extreme loading of wind turbines.
AMS 2000 Subject Classification Primary—60G15, 60G70, 62G32; Secondary—62P30 相似文献
8.
In this paper we derive large-buffer asymptotics for a two-class Generalized Processor Sharing (GPS) model. We assume both
classes to have Gaussian characteristics. We distinguish three cases depending on whether the GPS weights are above or below
the average rate at which traffic is sent. First, we calculate exact asymptotic upper and lower bounds, then we calculate
the logarithmic asymptotics, and finally we show that the decay rates of the upper and lower bound match. We apply our results
to two special Gaussian models: the integrated Gaussian process and the fractional Brownian motion. Finally we derive the
logarithmic large-buffer asymptotics for the case where a Gaussian flow interacts with an on-off flow.
AMS Subject Classification Primary—60K25; Secondary—68M20, 60G15 相似文献
9.
For a Wiener field with an arbitrary finite number of parameters, we construct the law of the iterated logarithm in the functional
form. We consider the problem for random fields of a certain type to reside within curvilinear boundaries without assuming
that the Cairoli—Walsh condition is satisfied.
Donetsk University, Donetsk. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 7, pp. 883–894, July, 1997. 相似文献
10.
Marco Castrillón López Jerrold E. Marsden 《Annals of Global Analysis and Geometry》2008,34(3):263-285
Reduction for field theories with symmetry can be done either covariantly—that is, on spacetime—or dynamically—that is, after
spacetime is split into space and time. The purpose of this article is to show that these two reduction procedures are, in
an appropriate sense, equivalent for a class of field theories whose fields take values in a principal bundle. One can think
of this class of field theories as including examples such as a “sea of rigid bodies” with and appropriate interbody coupling
potential. 相似文献
11.
We calculate the spectra and spectral measures associated to random walks on restricted wreath products G wr , with G a finite group, by calculating the Kesten—von Neumann—Serre spectral measures for the random walks on Schreier graphs of certain groups generated by automata. This generalises the work of Grigorchuk and Żuk on the lamplighter group. In the process we characterise when the usual spectral measure for a group generated by an automaton coincides with the Kesten—von Neumann—Serre spectral measure. 相似文献
12.
Ermanno Marchionna 《Annali di Matematica Pura ed Applicata》1956,41(1):43-71
Sunto Si indica e si applica un metodo per la ricerca effettiva del gruppo fondamentale G di una curva algebrica Φ, e si mostra
come — una volta trovato G — si risolvano non solo il problema dei piani multipli F diramati da Φ, ma anche altri problemi
connessi, di cui il principale è la determinazione delle funzioni algebriche prive di curva diramante sopra una corrispondente
superficie.
Si mostra tra l'altro — con costruzione diretta — come si possa modificare la curva di diramazione del piano multiplo generale
(cioè il suo gruppo fondamentale) affinchè sorgano su di esso cicli diramanti. 相似文献
13.
We consider biased random walk on supercritical percolation clusters in ℤ2. We show that the random walk is transient and that there are two speed regimes: If the bias is large enough, the random
walk has speed zero, while if the bias is small enough, the speed of the random walk is positive.
Received: 20 November 2002 / Revised version: 17 January 2003
Published online: 15 April 2003
Research supported by Microsoft Research graduate fellowship.
Research partially supported by the DFG under grant SPP 1033.
Research partially supported by NSF grant #DMS-0104073 and by a Miller Professorship at UC Berkeley.
Mathematics Subject Classification (2000): 60K37; 60K35; 60G50
Key words or phrases: Percolation – Random walk 相似文献
14.
New multiplicative and statistically self-similar measures μ are defined on ℝ as limits of measure-valued martingales. Those
martingales are constructed by multiplying random functions attached to the points of a statistically self-similar Poisson
point process defined in a strip of the plane. Several fundamental problems are solved, including the non-degeneracy and the
multifractal analysis of μ. On a bounded interval, the positive and negative moments of diverge under broad conditions.
First received: 14 September 1999 / Resubmited: 27 June 2001 / Revised version: 30 May 2002 / Published online: 30 September
2002
Mathematics Subject Classification (2002): 28A80, 60G18, 60G44, 60G55, 60G57
Key words or phrases: Random measures – Multifractal analysis – Continuous time martingales – Statistically self-similar Poisson point processes 相似文献
15.
Vittorio Dalla Volta 《Annali di Matematica Pura ed Applicata》1954,37(1):291-332
Sunto Si studia la nota metrica hermitiana, generalizzante la metrica iperbolica, che si incontra nella teoria delle funzioni di
p≥1 variabili complesse. — Nella p. I si determina, per via elementare, il gruppo continuo G di movimenti col massimo numero
di parametri ammesso dalla metrica considerata. — Nella p. II si studiano invece le faccette piane a curvatura nulla: tale
ricerca che è stata iniziata daF. Conforto — e condotta a termine daB. Segre per p=2 — viene qui completata, per ogni p, caratterizzando le faccette in questione rispetto al gruppo G, e dando delle
medesime una costruzione geometrica. 相似文献
16.
In cooperative dynamic games, a stringent condition—that of subgame consistency—is required for a dynamically stable cooperative solution. In particular, under a subgame-consistent cooperative solution
an extension of the solution policy to a subgame starting at a later time with a state brought about by prior optimal behavior
will remain optimal. This paper extends subgame-consistent solutions to dynamic (discrete-time) cooperative games with random
horizon. In the analysis, new forms of the Bellman equation and the Isaacs–Bellman equation in discrete-time are derived.
Subgame-consistent cooperative solutions are obtained for this class of dynamic games. Analytically tractable payoff distribution
mechanisms, which lead to the realization of these solutions, are developed. This is the first time that subgame-consistent
solutions for cooperative dynamic games with random horizon are presented. 相似文献
17.
A.Yu. Morozov 《Theoretical and Mathematical Physics》2010,162(1):1-33
We briefly review the basic properties of unitary matrix integrals, using three matrix models to analyze their properties:
the ordinary unitary, the Brezin—Gross—Witten, and the Harish—Chandra—Itzykson—Zuber models. We especially emphasize the nontrivial
aspects of the theory, from the De Witt’Hooft anomaly in unitary integrals to the problem of calculating correlators with
the Itzykson-Zuber measure. We emphasize the method of character expansions as a technical tool. Unitary integrals are still
insufficiently investigated, and many new results should be expected as this field attracts increased attention. 相似文献
18.
T.A. Springer 《Transformation Groups》2006,11(3):539-545
If G is a group and
an automorphism of G, one has the twisted conjugation action of G on itself
This paper collects a number of results — more or less well known — for the case that G is a simply connected semisimple
group. 相似文献
19.
20.
We consider a threshold autoregressive stochastic volatility model where the driving noises are sequences of iid regularly
random variables. We prove that both the right and the left tails of the marginal distribution of the log-volatility process
(αt)t are regularly varying with tail exponent −α with α > 0. We also determine the exact values of the coefficients in the tail behaviour of the process (αt)t.
AMS 2000 Subject Classification. Primary—62G32, 62PO5 相似文献