共查询到17条相似文献,搜索用时 0 毫秒
1.
For the Poisson line process the empirical polygon is defined thanks to ergodicity and laws of large numbers for some characteristics,
such as the number of edges, the perimeter, the area, etc... One also has, still thanks to the ergodicity of the Poisson line
process, a canonical relation between this empirical polygon and the polygon containing a given point. The aim of this paper
is to provide numerical simulations for both methods: in a previous paper (Paroux, Advances in Applied Probability, 30:640–656, 1998) one of the authors proved central limit theorems for some geometrical quantities associated with this empirical Poisson
polygon, we provide numerical simulations for this phenomenon which generates billions of polygons at a small computational
cost. We also give another direct simulation of the polygon containing the origin, which enables us to give further values
for empirical moments of some geometrical quantities than the ones that were known or computed in the litterature.
This work was partially supported by the PSMN at ENS-Lyon. 相似文献
2.
A linear birth–growth process is generated by an inhomogeneous Poisson process on ℝ × [0, ∞). Seeds are born randomly according to the Poisson process. Once a seed is born, it commences immediately to grow bidirectionally with a constant speed. The positions occupied by growing intervals are regarded as covered. New seeds continue to form on the uncovered part of ℝ. This paper shows that the total number of seeds born on a very long interval satisfies the strong invariance principle and some other strong limit theorems. Also, a gap (an unproved regularity condition) in the proof of the central limit theory in [5] is filled in. 相似文献
3.
Anatoliy Malyarenko 《Journal of Theoretical Probability》2006,19(2):263-288
We prove a general functional limit theorem for multiparameter fractional Brownian motion. The functional law of the iterated
logarithm, functional Lévy’s modulus of continuity and many other results are its particular cases. Applications to approximation
theory are discussed.
相似文献
4.
5.
Let W be a non-negative random variable with EW=1, and let {W
i
} be a family of independent copies of W, indexed by all the finite sequences i=i
1i
n
of positive integers. For fixed r and n the random multiplicative measure
n
r
has, on each r-adic interval
at nth level, the density
with respect to the Lebesgue measure on [0,1]. If EW log Wr, the sequence {
n
r
}
n
converges a.s. weakly to the Mandelbrot measure
r
. For each fixed 1n, we study asymptotic properties for the sequence of random measures {
n
r
}
r
as r. We prove uniform laws of large numbers, functional central limit theorems, a functional law of iterated logarithm, and large deviation principles. The function-indexed processes
is a natural extension to a tree-indexed process at nth level of the usual smoothed partial-sum process corresponding to n=1. The results extend the classical ones for {
1
r
}
r
, and the recent ones for the masses of {
r
}
r
established in Ref. 23. 相似文献
6.
Krzysztof Choromanski 《Journal of Graph Theory》2013,74(1):122-132
A celebrated unresolved conjecture of Erdös and Hajnal (see Discrete Appl Math 25 (1989), 37–52) states that for every undirected graph H, there exists , such that every graph on n vertices which does not contain H as an induced subgraph contains either a clique or an independent set of size at least . In (Combinatorica (2001), 155–170), Alon et al. proved that this conjecture was equivalent to a similar conjecture about tournaments. In the directed version of the conjecture cliques and stable sets are replaced by transitive subtournaments. For a fixed undirected graph H, define to be the supremum of all ε for which the following holds: for some n0 and every every undirected graph with vertices not containing H as an induced subgraph has a clique or independent set of size at least . The analogous definition holds if H is a tournament. We call the Erdös–Hajnal coefficient of H. The Erdös–Hajnal conjecture is true if and only if for every H. We prove in this article that:
- the Erdös–Hajnal coefficient of every graph H is at most ,
- there exists such that the Erdös–Hajnal coefficient of almost every tournament T on k vertices is at most , i.e. the proportion of tournaments on k vertices with the coefficient exceeding goes to 0 as k goes to infinity.
7.
Wojciech Samotij 《Random Structures and Algorithms》2014,44(3):269-289
Two years ago, Conlon and Gowers, and Schacht proved general theorems that allow one to transfer a large class of extremal combinatorial results from the deterministic to the probabilistic setting. Even though the two papers solve the same set of long‐standing open problems in probabilistic combinatorics, the methods used in them vary significantly and therefore yield results that are not comparable in certain aspects. In particular, the theorem of Schacht yields stronger probability estimates, whereas the one of Conlon and Gowers also implies random versions of some structural statements such as the famous stability theorem of Erd?s and Simonovits. In this paper, we bridge the gap between these two transference theorems. Building on the approach of Schacht, we prove a general theorem that allows one to transfer deterministic stability results to the probabilistic setting. We then use this theorem to derive several new results, among them a random version of the Erd?s‐Simonovits stability theorem for arbitrary graphs, extending the result of Conlon and Gowers, who proved such a statement for so‐called strictly 2‐balanced graphs. The main new idea, a refined approach to multiple exposure when considering subsets of binomial random sets, may be of independent interest.Copyright © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 44, 269‐289, 2014 相似文献
8.
Zheng Yan LIN Wen Sheng WANG Kyo Shin HWANG 《数学学报(英文版)》2006,22(6):1767-1780
In this paper, we obtain functional limit theorems for d-dimensional FBM in HSlder norm via estimating large deviation probabilities for d-dimensional FBM in HSlder norm. 相似文献
9.
10.
Klaus Ziegler 《Journal of multivariate analysis》1997,62(2):233-272
Functional central limit theorems for triangular arrays of rowwise independent stochastic processes are established by a method replacing tail probabilities by expectations throughout. The main tool is a maximal inequality based on a preliminary version proved by P. Gaenssler and Th. Schlumprecht. Its essential refinement used here is achieved by an additional inequality due to M. Ledoux and M. Talagrand. The entropy condition emerging in our theorems was introduced by K. S. Alexander, whose functional central limit theorem for so-calledmeasure-like processeswill be also regained. Applications concern, in particular, so-calledrandom measure processeswhich include function-indexed empirical processes and partial-sum processes (with random or fixed locations). In this context, we obtain generalizations of results due to K. S. Alexander, M. A. Arcones, P. Gaenssler, and K. Ziegler. Further examples include nonparametric regression and intensity estimation for spatial Poisson processes. 相似文献
11.
12.
Gutti Jogesh Babu Eugenijus Manstavičius 《Annals of the Institute of Statistical Mathematics》2002,54(3):607-620
The Ewens sampling formula in population genetics can be viewed as a probability measure on the group of permutations of a finite set of integers. Functional limit theory for processes defined through partial sums of dependent variables with respect to the Ewens sampling formula is developed. Techniques from probabilistic number theory are used to establish necessary and sufficient conditions for weak convergence of the associated dependent process to a process with independent increments. Not many results on the necessity part are known in the literature. 相似文献
13.
Ky Fan 《Set-Valued Analysis》1999,7(1):1-6
This is a continuation of paper in Adv. Appl. Math. 22 (1999), 219–226, on an antipodal theorem for sets Dn in Rn bounded by a finite number of spheres. Here this theorem is first applied to set-valued mappings from Dn to the boundary of an (n + 1)-cube or a d- dimensional octahedron. Next, the antipodal theorem is reformulated in terms of real continuous functions on Dn, together with applications to the classical theorems of Borsuk–Ulam and Lusternik–Schnirelmann–Borsuk. 相似文献
14.
Let X = (Xt, t 0) be a mean zero stationary Gaussian process with variance one, assumed to satisfy some conditions on its covariance function r. Central limit theorems and asymptotic variance formulas are provided for estimators of the square root of the second spectral moment of the process and for the number of maxima in an interval, with some applications in hydroscience. A consistent estimator of the asymptotic variance is proposed for the number of maxima. 相似文献
15.
Positive ground state solutions for a class of Schrödinger–Poisson systems with sign‐changing and vanishing potential 下载免费PDF全文
Hongliang Liu Haibo Chen Qizhen Xiao 《Mathematical Methods in the Applied Sciences》2017,40(6):1937-1948
This paper deals with the following Schrödinger–Poisson systems where λ, ν are positive parameters and V(x) is sign‐changing and may vanish at infinity. Under some suitable assumptions, the existence of positive ground state solutions is obtained by using variational methods. Our main results unify and improve the recent ones in the literatures. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
16.
Consider a double array
of i.i.d. random variables with mean and variance
and set
. Let
denote the empirical distribution function of Z1, n
,..., Z
N, n
and let be the standard normal distribution function. The main result establishes a functional law of the iterated logarithm for
, where n=n(N) as N. For the proof, some lemmas are derived which may be of independent interest. Some corollaries of the main result are also presented. 相似文献
17.
J. Sunklodas 《Lithuanian Mathematical Journal》2001,41(3):292-305
We derive lower bounds for Lp norms
, in the central limit theorem for independent and m–dependent random variables with finite fifth order absolute moments and for independent and m–dependent identically distributed random variables with fourth order moments. 相似文献