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1.
We consider a general k-dimensional discounted infinite server queueing process (alternatively, an incurred but not reported claim process) where the multivariate inputs (claims) are given by a k-dimensional finite-state Markov chain and the arrivals follow a renewal process. After deriving a multidimensional integral equation for the moment-generating function jointly to the state of the input at time t given the initial state of the input at time 0, asymptotic results for the first and second (matrix) moments of the process are provided. In particular, when the interarrival or service times are exponentially distributed, transient expressions for the first two moments are obtained. Also, the moment-generating function for the process with deterministic interarrival times is considered to provide more explicit expressions. Finally, we demonstrate the potential of the present model by showing how it allows us to study semi-Markovian modulated infinite server queues where the customers (claims) arrival and service (reporting delay) times depend on the state of the process immediately before and at the switching times. 相似文献
2.
In this article, we consider exponential random geometric graph, in d-dimensional space ( d≥2). The main results are almost-sure asymptotic rates of convergence/divergence for the maximum and minimum vertex degrees of graph, when edge distance varies with the number of vertices. 相似文献
3.
Summary We consider the estimation of frequency ω of a sinusoidal oscillation contaminated by a stationary noise under a random sampling
scheme according to a stationary point process N. We prove the strong consistency and the asymptotic normality for a certain estimator of ω. Then we apply these results to
the case where N is a stationary delayed renewal process. 相似文献
4.
We obtain an information-type inequality and a strong law for a wide class of statistical distances between empirical estimates and random measures based on Voronoi tessellations. This extends some basic results in the asymptotic theory of sample spacings, when the cells of the Voronoi tessellation are interpreted as d-dimensional spacings. 相似文献
5.
This paper presents formulas and asymptotic expansions for the expected number of vertices and the expected volume of the
convex hull of a sample of n points taken from the uniform distribution on a d-dimensional ball. It is shown that the expected number of vertices is asymptotically proportional to n
(d−1)/(d+1), which generalizes Rényi and Sulanke’s asymptotic rate n
(1/3) for d=2 and agrees with Raynaud’s asymptotic rate n
(d−1)/(d+1) for the expected number of facets, as it should be, by Bárány’s result that the expected number of s-dimensional faces has order of magnitude independent of s. Our formulas agree with the ones Efron obtained for d=2 and 3 under more general distributions. An application is given to the estimation of the probability content of an unknown
convex subset of R
d
. 相似文献
6.
In this paper the comparison result for the heat kernel on Riemannian manifolds with lower Ricci curvature bound by Cheeger and Yau (1981) is extended to locally compact path metric spaces ( X, d) with lower curvature bound in the sense of Alexandrov and with sufficiently fast asymptotic decay of the volume of small geodesic balls. As corollaries we recover Varadhan's short time asymptotic formula for the heat kernel (1967) and Cheng's eigenvalue comparison theorem (1975). Finally, we derive an integral inequality for the distance process of a Brownian Motion on ( X, d) resembling earlier results in the smooth setting by Debiard, Geavau and Mazet (1975). 相似文献
7.
We consider the problem of the density and drift estimation by the observation of a trajectory of an
\mathbb Rd{\mathbb{R}^{d}}-dimensional homogeneous diffusion process with a unique invariant density. We construct estimators of the kernel type based
on discretely sampled observations and study their asymptotic distribution. An estimate of the rate of normal approximation
is given. 相似文献
8.
This paper addresses the problem of testing goodness-of-fit for several important multivariate distributions: (I) Uniform
distribution on p-dimensional unit sphere; (II) multivariate standard normal distribution; and (III) multivariate normal distribution with
unknown mean vector and covariance matrix. The average projection type weighted Cramér-von Mises test statistic as well as
estimated and weighted Cramér-von Mises statistics for testing distributions (I), (II) and (III) are constructed via integrating
projection direction on the unit sphere, and the asymptotic distributions and the expansions of those test statistics under
the null hypothesis are also obtained. Furthermore, the approach of this paper can be applied to testing goodness-of-fit for
elliptically contoured distributions. 相似文献
9.
In this article, some asymptotic formulas of the finite-time ruin probability for a two-dimensional renewal risk model are obtained. In the model, the distributions of two claim amounts belong to the intersection of the long-tailed distributions class and the dominated varying distributions class and the claim arrival-times are extended negatively dependence structures. Assumption that the claim arrivals of two classes are governed by a common renewal counting process. The asymptotic formulas hold uniformly for t ∈ [ f( x), ∞), where f( x) is an infinitely increasing function. 相似文献
10.
Let n random points be given with uniform distribution in the d-dimensional unit cube [0,1] d. The smallest parallelepiped A which includes all the n random points is dealt with. We investigate the asymptotic behavior of the volume of A as n tends to . Using a point process approach, we derive also the asymptotic behavior of the volumes of the k-th smallest parallelepipeds A
n
(k)
which are defined by iteration. Let A
n = A
n
(1)
. Given A
n
(k,-,1)
delete the random points X
i which are on the boundary A
n
(k,-,1)
, and construct the smallest parallelepiped which includes the inner points of A
n
(k,-,1)
, this defines A
n
(k)
. This procedure is known as peeling of the parallelepiped A n. 相似文献
11.
We prove a limit theorem for the maximum interpoint distance (also called the diameter) for a sample of n i.i.d. points in the unit d-dimensional ball for d≥2. The results are specialised for the cases when the points have spherical symmetric distributions, in particular, are uniformly
distributed in the whole ball and on its boundary. Among other examples, we also give results for distributions supported
by pointed sets, such as a rhombus or a family of segments.
相似文献
12.
Suppose we have a renewal process observed over a fixed length of time starting from a random time point and only the times
of renewals that occur within the observation window are recorded. Assuming a parametric model for the renewal time distribution
with parameter θ, we obtain the likelihood of the observed data and describe the exact and asymptotic behavior of the Fisher information (FI)
on θ contained in this window censored renewal process. We illustrate our results with exponential, gamma, and Weibull models
for the renewal distribution. We use the FI matrix to determine optimal window length for designing experiments with recurring
events when the total time of observation is fixed. Our results are useful in estimating the standard errors of the maximum
likelihood estimators and in determining the sample size and duration of clinical trials that involve recurring events associated
with diseases such as lupus. 相似文献
13.
We consider so-called Tusnády’s problem in dimension d: Given an n-point set P in R d , color the points of P red or blue in such a way that for any d-dimensional interval B, the number of red points in differs from the number of blue points in by at most Δ, where should be as small as possible. We slightly improve previous results of Beck, Bohus, and Srinivasan by showing that , with a simple proof. The same asymptotic bound is shown for an analogous problem where B is allowed to be any translated and scaled copy of a fixed convex polytope A in R d . Here the constant of proportionality depends on A and we give an explicit estimate. The same asymptotic bounds also follow for the Lebesgue-measure discrepancy, which improves and simplifies results of Beck and of Károlyi. 相似文献
14.
In [H. Taniguchi, On d-dimensional dual hyperovals in PG(2 d,2), Innov. Incidence Geom., in press], we construct d-dimensional dual hyperovals in PG(2 d,2) from quasifields of characteristic 2. In this note, we show that, if d-dimensional dual hyperovals in PG(2 d,2) constructed from nearfields are isomorphic, then those nearfields are isomorphic. Some results on dual hyperovals constructed from quasifields are also proved. 相似文献
15.
We consider so-called Tusnády’s problem in dimension d: Given an n-point set P in R
d
, color the points of P red or blue in such a way that for any d-dimensional interval B, the number of red points in differs from the number of blue points in by at most Δ, where should be as small as possible. We slightly improve previous results of Beck, Bohus, and Srinivasan by showing that , with a simple proof. The same asymptotic bound is shown for an analogous problem where B is allowed to be any translated and scaled copy of a fixed convex polytope A in R
d
. Here the constant of proportionality depends on A and we give an explicit estimate. The same asymptotic bounds also follow for the Lebesgue-measure discrepancy, which improves
and simplifies results of Beck and of Károlyi.
Received 17 November 1997; in revised form 30 July 1998 相似文献
16.
We establish a close relationship between isoperimetric inequalities for convex bodies and asymptotic shapes of large random
polytopes, which arise as cells in certain random mosaics in d-dimensional Euclidean space. These mosaics are generated by Poisson hyperplane processes satisfying a few natural assumptions
(not necessarily stationarity or isotropy). The size of large cells is measured by a class of general functionals. The main
result implies that the asymptotic shapes of large cells are completely determined by the extremal bodies of an inequality
of isoperimetric type, which connects the size functional and the expected number of hyperplanes of the generating process
hitting a given convex body. We obtain exponential estimates for the conditional probability of large deviations of zero cells
from asymptotic or limit shapes, under the condition that the cells have large size.
This work was supported in part by the European Network PHD, FP6 Marie Curie Actions, RTN, Contract MCRN-511953.
Received: May 2005 Accepted: September 2005 相似文献
17.
Constructions and nonexistence conditions for multi-dimensional Golay complementary array pairs are reviewed. A construction
for a d-dimensional Golay array pair from a ( d + 1)-dimensional Golay array pair is given. This is used to explain and expand previously known constructive and nonexistence
results in the binary case.
相似文献
18.
We consider the flow of a stochastic differential equation on d-dimensional Euclidean space. We show that if the Lie algebra generated by its diffusion vector fields is finite dimensional
and solvable, then the flow is conjugate to the flow of a non-autonomous random differential equation, i.e. one can be transformed
into the other via a random diffeomorphism of d-dimensional Euclidean space. Viewing a stochastic differential equation in this form which appears closer to the setting
of ergodic theory, can be an advantage when dealing with asymptotic properties of the system. To illustrate this, we give
sufficient criteria for the existence of global random attractors in terms of the random differential equation, which are
applied in the case of the Duffing-van der Pol oscillator with two independent sources of noise.
Received: 25 May 1999 / Revised version: 19 October 2000 / Published online: 26 April 2001 相似文献
19.
We provide estimates for the fixed point ratios in the permutation representations of a finite classical group over a field of order q on k-subspaces of its natural n-dimensional module. For sufficiently large n, each element must either have a negligible ratio or act linearly with a large eigenspace. We obtain an asymptotic estimate in the latter case, which in most cases is q
–dk where d is the codimension of the large eigenspace. The results here are tailored for our forthcoming proof of a conjecture of Guralnick and Thompson on composition factors of monodromy groups. 相似文献
20.
Recently, Zhao et al. (in Fuzzy Optimization and Decision Making 2007 6, 279–295) presented a fuzzy random elementary renewal
theorem and fuzzy random renewal reward theorem in the fuzzy random process. In this paper, we study the convergence of fuzzy
random renewal variable and of the total rewards earned by time t with respect to the extended Hausdorff metrics d
∞ and d
1. Using this convergence information and applying the uniform convergence theorem, we provide some new versions of the fuzzy
random elementary renewal theorem and the fuzzy random renewal reward theorem. 相似文献
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