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1.
设 { ( Xi,Yi) ,i≥ 1 }是独立同分布二维随机向量列 ,其共同分布函数为 F.设 F属于 G的吸引场 ,本文假定边缘分布满足 Von-Mises条件 ,主要考虑二维极大值向量 Mn 密度收敛局部一致成立的问题 .本文将 Resnick[3 ]的结果推广到了二维情形 相似文献
3.
Gerold Alsmeyer 《Mathematical Methods of Operations Research》1986,30(3):A111-A134
Let
1, 2, ... be a sequence of i.i.d. random variables with positive mean
and finite variance
and letr(b), b0, be real numbers tending to 0 asb . Definings
n=1+...+n andS
n=Sn(b)=sn+r(b)n, the stopping time =(b)=inf {n>/1:Sn >b} whereb=b(b) , will be considered with special regard to the excess over the boundaryR
b=s+r(b)–b. It turns out that the limiting distribution ofR
b is the same as in the caser(b)0 for allb. Proving this, Blackwell's renewal theorem and its integral version have to be established first in the above stated situation. Finally, an expansion ofE to vanishing terms asb will be provided and applied to some examples arising in economics.
Zusammenfassung Seien 1, 2, ... unabhängige identisch verteilte Zufallsgrößen mit positivem Erwartungswert und endlicher Varianz sowier(b), b0, reelle Zahlen mitr(b)0 für b. Sei ferners 1, s2, ... der zugehörige Summenprozeß,S n= Sn(b)=sn+r(b)n fürn1 und =(b)=inf {n1: Sn>b, wobeib=b(b) fürb . Es wird gezeigt, daß die asymptotische Verteilung des ExzessesR b=s +r(b) –b mit der im Fallr(·)0 übereinstimmt. Dazu werden sowohl das Blackwellsche Erneuerungstheorem als auch seine Integralversion in der vorher beschriebenen parameterabhängigen Situation geeignet formuliert und bewiesen. Als Folgerung ergibt sich dann eine asymptotische Entwicklung vonE(b) fürb bis zu Termen o(1). Anh- and einiger Beispiele aus dem ökonomischen Bereich wird schließlich noch aufgezeigt, wo Approximationen fürE(b) von Interesse sein können.相似文献
4.
Li Wei 《中国科学A辑(英文版)》2009,52(7):1539-1545
The ruin probability of the renewal risk model with investment strategy for a capital market index is investigated in this
paper. For claim sizes with common distribution of extended regular variation, we study the asymptotic behaviour of the ruin
probability. As a corollary, we establish a simple asymptotic formula for the ruin probability for the case of Pareto-like
claims.
This work was supported by National Natural Science Foundation of China (Grant Nos. 10571167, 70501028), the Beijing Sustentation
Fund for Elitist (Grant No. 20071D1600800421), the National Social Science Foundation of China (Grant No. 05&ZD008) and the
Research Grant of Renmin University of China (Grant No. 08XNA001) 相似文献
5.
Using two kinds of multivariate regular variation we prove several Abel-Tauber theorems for the Laplace transform of functions in several variables. We generalize some power series results of Alpar and apply our results in multivariate renewal theory. 相似文献
6.
Dmitry Korshunov 《Journal of Theoretical Probability》2008,21(1):234-245
We consider a time-homogeneous real-valued Markov chain X
n
, n≥0. Suppose that this chain is transient, that is, X
n
generates a σ-finite renewal measure. We prove the key renewal theorem under the condition that this chain has jumps that are asymptotically
homogeneous at infinity and asymptotically positive drift. 相似文献
7.
Steven J. Sepanski 《Journal of Theoretical Probability》1994,7(4):857-866
For independent identically distributed random vectors,X
i
, we give necessary and sufficient probabilistic conditions for their common distribution to belong to the Generalized Domain of Attraction of the multivariate normal law. The first condition says that after projecting onto any direction, , the sum of squares,
i
1=1
X
i
, 2, properly normalized, converges to one in probability uniformly over the unit sphere. The second condition says that max X
i
, 2/
n
i=1
X
i
, 2 converges to zero in probability uniformly over the unit sphere. 相似文献
8.
Dominik Kortschak Hansjörg Albrecher 《Methodology and Computing in Applied Probability》2009,11(3):279-306
In this paper we extend some results about the probability that the sum of n dependent subexponential random variables exceeds a given threshold u. In particular, the case of non-identically distributed and not necessarily positive random variables is investigated. Furthermore
we establish criteria how far the tail of the marginal distribution of an individual summand may deviate from the others so
that it still influences the asymptotic behavior of the sum. Finally we explicitly construct a dependence structure for which,
even for regularly varying marginal distributions, no asymptotic limit of the tail of the sum exists. Some explicit calculations
for diagonal copulas and t-copulas are given.
Dominik Kortschak was supported by the Austrian Science Fund Project P18392. 相似文献
9.
This paper studies a continuous-time multidimensional risk model with constant force of interest and dependence structures among random factors involved. The model allows a general dependence among the claim-number processes from different insurance businesses. Moreover, we utilize the framework of multivariate regular variation to describe the dependence and heavy-tailed nature of the claim sizes. Some precise asymptotic expansions are derived for both finite-time and infinite-time ruin probabilities. 相似文献
10.
The ruin probability of the renewal model with constant interest force and negatively dependent heavy-tailed claims 总被引:2,自引:0,他引:2
Recently, Tang [Tang, Q., 2005a. Asymptotic ruin probabilities of the renewal model with constant interest force and regular variation. Scand. Actuar. J. (1), 1–5] obtained a simple asymptotic formula for the ruin probability of the renewal risk model with constant interest force and regularly varying tailed claims. In this paper, we use a completely different approach to extend Tang’s result to the case in which the claims are pairwise negatively dependent and extended regularly varying tailed. 相似文献
11.
Summary LetF(x) be a nonarithmetic c.d.f. on (0, ) such that 1 —F(x)=x
–
L(x), whereL(x) is slowly varying and 01. Leta(x) be regularly varying with exponent 1. A strong renewal theorem (of Blackwell type) for generalized renewal functions of the form
is proved here, thus extending the recent work of Embrechts, Maejima and Omey [1] and that of Erickson [4].Kevin K. Anderson is now at Lawrence Livermore National Laboratory, P.O. Box 808, Livermore, CA 914550 USA. His research was performed in part under the auspices of the U.S. Department of Energy at LLNL under Contract W-7405-Eng-48.The research of Krishna B. Athreya was supported in part by NSF Grants DMS-8502311 and DMS-8706319. 相似文献
12.
Let
be a sequence of independent identically distributed positive random variables with O-regularly varying distribution F at 0. Given a sequence
of positive numbers, we show that
belongs to the Type I domain of attraction of extremes for minima, by means of relating the asymptotic behaviour of P{S < } as 0, to that of E{e-S/}. Our contribution is that we dispense with the unnatural moment condition from the literature, that F has finite variance. This in turn permits a novel application to lower tails of -stable distributions on Hilbert space.AMS 2000 Subject Classification. Primary—60G50, 60G70, Secondary—60B12, 60E07, 60F05, 60G52Research supported by NFR Grant M 650-19981841/2000, and by M.R. Leadbetter 相似文献
13.
Steven G. Krantz Harold R. Parks 《Journal of Mathematical Analysis and Applications》2008,340(2):1263-1270
The classical Lagrange inversion theorem is a concrete, explicit form of the implicit function theorem for real analytic functions. An explicit construction shows that the formula is not true for all merely smooth functions. The authors modify the Lagrange formula by replacing the smooth function by its Maclaurin polynomials. The resulting modified Lagrange series is, in analogy to the Maclaurin polynomials, an approximation to the solution function accurate to o(xN) as x→0. 相似文献
14.
设N(t)为一更新计数过程,本文得到了在时间间隔有有限期望的情形下,关于N(t)的任意阶矩的一个等价式,该结果可以看成是基本更新定理的推广。对于时间间隔为轻尾的(矩母函数存在)或者是一类特殊的重尾族(确切地,ERV族)时,得到了更加精细的结果。 相似文献
15.
Gut and Sp?taru (J. Math. Anal. Appl. 248 (2000) 233-246) proved a precise asymptotic theorem for random variables in the normal domain of attraction of some stable distribution with exponent α, 1<α?2. They also conjectured that the theorem should hold for the general case of the domain of attraction of a stable distribution. In this paper, we shall provide an example to deny their conjecture and study some further properties. 相似文献
16.
Mark M. Meerschaert 《Journal of Theoretical Probability》1994,7(4):793-798
A sequence of independent and identically distributed random vectorsX
n
on
k
is said to belong to the generalized domain of attraction of a nondegenerate random vectorY on
k
provided that there exist linear operatorsA
n
on
k
and nonrandom constantsb
n
k
such that the centered and normalized partial sumsA
n
(X
1++X
n
–b
n
converge in distribution toY. In this paper we show that the sequence of norming operatorsA
n
can always be chosen to vary regularly.Partially supported by NSF Grant DMS-91-03131 at Albion College. 相似文献
17.
Jorge Mujica Paula Takatsuka 《Proceedings of the American Mathematical Society》2007,135(4):1141-1144
We show that if is a starlike domain in a Banach space and is a family of holomorphic functions on that omit two distinct values and is bounded at the origin, then is uniformly bounded on each -bounded set.
18.
In this paper we present an exact method for computing the Weibull renewal function and its derivative for application in maintenance optimization. The computational method provides a solid extension to previous work by which an approximation to the renewal function was used in a Bayesian approach to determine optimal replacement times. In the maintenance scenario, under the assumption an item is replaced by a new one upon failure, the underlying process between planned replacement times is a renewal process. The Bayesian approach takes into account failure and survival information at each planned replacement stage to update the optimal time until the next planned replacement. To provide a simple approach to carry out in practice, we limit the decision process to a one‐step optimization problem in the sequential decision problem. We make the Weibull assumption for the lifetime distribution of an item and calculate accurately the renewal function and its derivative. A method for finding zeros of a function is adapted to the maintenance optimization problem, making use of the availability of the derivative of the renewal function. Furthermore, we develop the maximum likelihood estimate version of the Bayesian approach and illustrate it with simulated examples. The maintenance algorithm retains the adaptive concept of the Bayesian methodology but reduces the computational need. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
19.
Stathis Chadjiconstantinidis 《Insurance: Mathematics and Economics》2007,41(1):41-52
We obtain lower and upper bounds for the severity of ruin in the renewal (Sparre Andersen) model of risk theory. We present two types of bounds: (i) bounds applicable generally; and (ii) exponential bounds for the case where the adjustment coefficient of the risk process exists. Many of these bounds are obtained using existing bounds and the integral equation for the severity of ruin. 相似文献
20.
A. A. Mogul’skii 《Siberian Mathematical Journal》2008,49(4):669-683
We obtain an integro-local limit theorem for the sum S(n) = ξ(1)+?+ξ(n) of independent identically distributed random variables with distribution whose right tail varies regularly; i.e., it has the form P(ξ≥t) = t ?β L(t) with β > 2 and some slowly varying function L(t). The theorem describes the asymptotic behavior on the whole positive half-axis of the probabilities P(S(n) ∈ [x, x + Δ)) as x → ∞ for a fixed Δ > 0; i.e., in the domain where the normal approximation applies, in the domain where S(n) is approximated by the distribution of its maximum term, as well as at the “junction” of these two domains. 相似文献