共查询到20条相似文献,搜索用时 46 毫秒
1.
M. Ivette Gomes 《Annals of the Institute of Statistical Mathematics》1984,36(1):71-85
Summary Let {X
n}n≧1 be a sequence of independent, identically distributed random variables. If the distribution function (d.f.) ofM
n=max (X
1,…,X
n), suitably normalized with attraction coefficients {αn}n≧1(αn>0) and {b
n}n≧1, converges to a non-degenerate d.f.G(x), asn→∞, it is of interest to study the rate of convergence to that limit law and if the convergence is slow, to find other d.f.'s
which better approximate the d.f. of(M
n−bn)/an thanG(x), for moderaten. We thus consider differences of the formF
n(anx+bn)−G(x), whereG(x) is a type I d.f. of largest values, i.e.,G(x)≡Λ(x)=exp (-exp(−x)), and show that for a broad class of d.f.'sF in the domain of attraction of Λ, there is a penultimate form of approximation which is a type II [Ф
α(x)=exp (−x−α), x>0] or a type III [Ψ
α(x)= exp (−(−x)α), x<0] d.f. of largest values, much closer toF
n(anx+bn) than the ultimate itself. 相似文献
2.
Zhu Xuexian 《分析论及其应用》1989,5(3):83-92
We show that if K(x,y)=Ω(x,y)/|x|n|y|m is a Calder n-Zygmund kerned on Rn×Rm, where Ω∈L2(Sn−1×Sm−1) and b(x,y) is any bounded function which is radial with x∈Rn and y∈Rm respectively, then b(x,y)K(x,y) is the kernel of a convolution operator which is bounded on Lp(Rn×Rm) for 1<p<∞ and n≧2, m≧2.
Project supported by NSFC 相似文献
3.
Henry Teicher 《Journal of Theoretical Probability》1995,8(4):779-793
Conditions are obtained for (*)E|S
T
|γ<∞, γ>2 whereT is a stopping time and {S
n=∑
1
n
,X
j
ℱ
n
,n⩾1} is a martingale and these ensure when (**)X
n
,n≥1 are independent, mean zero random variables that (*) holds wheneverET
γ/2<∞, sup
n≥1
E|X
n
|γ<∞. This, in turn, is applied to obtain conditions for the validity ofE|S
k,T
|γ<∞ and of the second moment equationES
k,T
2
=σ
2
EΣ
j=k
T
S
k−1,j−1
2
where
and {X
n
, n≥1} satisfies (**) and
,n≥1. The latter is utilized to elicit information about a moment of a stopping rule. It is also shown for i.i.d. {X
n
, n≥1} withEX=0,EX
2=1 that the a.s. limit set of {(n log logn)−k/2
S
k,n
,n≥k} is [0,2
k/2/k!] or [−2
k/2/k!] according ask is even or odd and this can readily be reformulated in terms of the corresponding (degenerate kernel)U-statistic
. 相似文献
4.
M. Ahsanullah 《Annals of the Institute of Statistical Mathematics》1978,30(1):429-433
A sequence {X
n,n≧1} of independent and identically distributed random variables with continuous cumulative distribution functionF(x) is considered.X
j is a record value of this sequence ifX
j>max (X
1, …,X
j−1). Let {X
L(n) n≧0} be the sequence of such record values. Some properties ofX
L(n) andX
L(n)−XL(n−1) are studied when {X
n,n≧1} has the exponential distribution. Characterizations of the exponential distribution are given in terms of the sequence
{X
L(n),n≧0}
The work was partly completed when the author was at the Department of Statistics, University of Brasilia, Brazil. 相似文献
5.
V. A. Kondratiev 《Journal of Mathematical Sciences》1997,85(6):2385-2401
The paper deals with a linear elliptic second-order equation in divergent form in a semi-infinite cylinder Ω=Ω×[0,∞), where
Ω is a bounded domain, Ω⊂ℝn−1, 0≤xn<∞. The solution under consideration satisfies the nonlinear boundary condition, ∂u/∂v+a0∣u∣q−1u=0, where ϖ/ϖν is the differentiation along the external conormal a0=const>0, q=const. The asymptotic behavior of the solution for xn→+∞ is studied. Bibliography: 15 titles.
Dedicated to O. A. Oleinik
The investigations described in this paper were supported in part by the Russian Foundation for Basic Research, project No.
93-011-16035, and by the International Science Foundation, grant MIE000.
Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 19, pp. 000-000, 0000. 相似文献
6.
Steve Kalikow 《Israel Journal of Mathematics》1990,71(1):33-54
It is shown here that a certain generalization of ann-step Markov chain is equivalent to the uniform convergence of the martingale {P(X
0|X
−1
X
−2···X
−n)}
n=1
∞
. Ergodic and probabilistic properties of this process are explored.
This work was initiated at SUNY/Albany. 相似文献
7.
V. F. Gaposhkin 《Mathematical Notes》1998,64(3):316-321
The asymptotic behavior asn → ∞ of the normed sumsσn =n
−1 Σ
k
=0n−1
Xk for a stationary processX = (X
n
,n ∈ ℤ) is studied. For a fixedε > 0, upper estimates for P(sup
k≥n
|σ
k
| ≥ε) asn → ∞ are obtained.
Translated fromMatematicheskie Zametki, Vol. 64, No. 3, pp. 366–372, September, 1998. 相似文献
8.
For a Tychonoff space X,we use ↓USC F(X) and ↓C F(X) to denote the families of the hypographs of all semi-continuous maps and of all continuous maps from X to I = [0,1] with the subspace topologies of the hyperspace Cld F(X × I) consisting of all non-empty closed sets in X × I endowed with the Fell topology.In this paper,we shall show that there exists a homeomorphism h:↓USC F(X) → Q = [1,1] ω such that h(↓CF(X))=c0 = {(xn)∈Q| lim n→∞ x n = 0} if and only if X is a locally compact separable metrizable space and the set of isolated points is not dense in X. 相似文献
9.
It is shown that ifA andB are non-empty subsets of {0, 1}
n
(for somenεN) then |A+B|≧(|A||B|)α where α=(1/2) log2 3 here and in what follows. In particular if |A|=2
n-1 then |A+A|≧3
n-1 which anwers a question of Brown and Moran. It is also shown that if |A| = 2
n-1 then |A+A|=3
n-1 if and only if the points ofA lie on a hyperplane inn-dimensions. Necessary and sufficient conditions are also given for |A +B|=(|A||B|)α. The above results imply the following improvement of a result of Talagrand [7]: ifX andY are compact subsets ofK (the Cantor set) withm(X),m(Y)>0 then λ(X+Y)≧2(m(X)m(Y))α wherem is the usual measure onK and λ is Lebesgue measure. This also answers a question of Moran (in more precise terms) showing thatm is not concentrated on any proper Raikov system. 相似文献
10.
Eliyahu Beller 《Israel Journal of Mathematics》1977,27(3-4):320-330
A generalization of the Blaschke product is constructed. This product enables one to factor out the zeros of the members of
certain non-Nevanlinna classes of functions analytic in the unit disc, so that the remaining (non-vanishing) functions still
belong to the same class. This is done for the classesA
−n (0<n<∞) andB
−n (0<n<2) defined as follows:f ∈A
−n iff |f(z)|≦C
f
(1−|z|)−n
,f ∈B
−n
iff |f(z)|≦exp {C
f
(1−|z|)−n
}, whereC
f
depends onf. 相似文献
11.
René L. Schilling 《Probability Theory and Related Fields》1998,112(4):565-611
Let (A,D(A)) be the infinitesimal generator of a Feller semigroup such that C
c
∞(ℝ
n
)⊂D(A) and A|C
c
∞(ℝ
n
) is a pseudo-differential operator with symbol −p(x,ξ) satisfying |p(•,ξ)|∞≤c(1+|ξ|2) and |Imp(x,ξ)|≤c
0Rep(x,ξ). We show that the associated Feller process {X
t
}
t
≥0 on ℝ
n
is a semimartingale, even a homogeneous diffusion with jumps (in the sense of [21]), and characterize the limiting behaviour
of its trajectories as t→0 and ∞. To this end, we introduce various indices, e.g., β∞
x
:={λ>0:lim
|ξ|→∞
|
x
−
y
|≤2/|ξ||p(y,ξ)|/|ξ|λ=0} or δ∞
x
:={λ>0:liminf
|ξ|→∞
|
x
−
y
|≤2/|ξ|
|ε|≤1|p(y,|ξ|ε)|/|ξ|λ=0}, and obtain a.s. (ℙ
x
) that lim
t
→0
t
−1/λ
s
≤
t
|X
s
−x|=0 or ∞ according to λ>β∞
x
or λ<δ∞
x
. Similar statements hold for the limit inferior and superior, and also for t→∞. Our results extend the constant-coefficient (i.e., Lévy) case considered by W. Pruitt [27].
Received: 21 July 1997 / Revised version: 26 January 1998 相似文献
12.
Katalin Marton 《Probability Theory and Related Fields》1998,110(3):427-439
Summary. Let X={X
i
}
i
=−∞
∞ be a stationary random process with a countable alphabet and distribution q. Let q
∞(·|x
−
k
0) denote the conditional distribution of X
∞=(X
1,X
2,…,X
n
,…) given the k-length past:
Write d(1,x
1)=0 if 1=x
1, and d(1,x
1)=1 otherwise. We say that the process X admits a joining with finite distance u if for any two past sequences −
k
0=(−
k
+1,…,0) and x
−
k
0=(x
−
k
+1,…,x
0), there is a joining of q
∞(·|−
k
0) and q
∞(·|x
−
k
0), say dist(0
∞,X
0
∞|−
k
0,x
−
k
0), such that
The main result of this paper is the following inequality for processes that admit a joining with finite distance:
Received: 6 May 1996 / In revised form: 29 September 1997 相似文献
13.
In this paper, we first consider a delay difference equation of neutral type of the form:
Δ(y
n
+ py
n−k
+ q
n
y
n−l
= 0 for n∈ℤ+(0) (1*)
and give a different condition from that of Yu and Wang (Funkcial Ekvac, 1994, 37(2): 241–248) to guarantee that every non-oscillatory solution of (1*) with p = 1 tends to zero as n→∞. Moreover, we consider a delay reaction-diffusion difference equation of neutral type of the form:
Δ1(u
n,m
+ pu
n−k,m
) + q
n,m
u
n−l,m
= a
2Δ2
2
u
n
+1,
m−1
for (n,m) ∈ℤ+ (0) ×Ω, (2*)
study various cases of p in the neutral term and obtain that if p≥−1 then every non-oscillatory solution of (2*) tends uniformly in m∈Ω to zero as n→∞; if p = −1 then every solution of (2*) oscillates and if p < −1 then every non-oscillatory solution of (2*) goes uniformly in m∈Ω to infinity or minus infinity as n→∞ under some hypotheses.
Received July 14, 1999, Revised August 10, 2000, Accepted September 30, 2000 相似文献
14.
In this paper, we consider the global existence, uniqueness and L
∞ estimates of weak solutions to quasilinear parabolic equation of m-Laplacian type u
t
− div(|∇u|
m−2∇u) = u|u|
β−1 ∫Ω |u|
α
dx in Ω × (0,∞) with zero Dirichlet boundary condition in tdΩ. Further, we obtain the L
∞ estimate of the solution u(t) and ∇u(t) for t > 0 with the initial data u
0 ∈ L
q
(Ω) (q > 1), and the case α + β < m − 1. 相似文献
15.
In this paper, we prove the algebraic independence of the reciprocal sums of odd terms in Fibonacci numbers ∑
n=1∞
F
2n−1−1, ∑
n=1∞
F
2n−1−2, ∑
n=1∞
F
2n−1−3 and write each ∑
n=1∞
F
2n−1−s
(s≥4) as an explicit rational function of these three numbers over ℚ. Similar results are obtained for various series including
the reciprocal sums of odd terms in Lucas numbers.
相似文献
16.
Artūras Dubickas 《Monatshefte für Mathematik》2009,137(2):271-284
We prove that, for any real numbers ξ ≠ 0 and ν, the sequence of integer parts [ξ2
n
+ ν], n = 0, 1, 2, . . . , contains infinitely many composite numbers. Moreover, if the number ξ is irrational, then the above sequence
contains infinitely many elements divisible by 2 or 3. The same holds for the sequence [ξ( − 2)
n
+ ν
n
], n = 0, 1, 2, . . . , where ν
0, ν
1, ν
2, . . . all lie in a half open real interval of length 1/3. For this, we show that if a sequence of integers x
1, x
2, x
3, . . . satisfies the recurrence relation x
n+d
= cx
n
+ F(x
n+1, . . . , x
n+d-1) for each n ≥ 1, where c ≠ 0 is an integer,
F(z1,...,zd-1) ? \mathbb Z[z1,...,zd-1],{F(z_1,\dots,z_{d-1}) \in \mathbb {Z}[z_1,\dots,z_{d-1}],} and lim
n→ ∞|x
n
| = ∞, then the number |x
n
| is composite for infinitely many positive integers n. The proofs involve techniques from number theory, linear algebra, combinatorics on words and some kind of symbolic computation
modulo 3. 相似文献
17.
Dale Umbach 《Annals of the Institute of Statistical Mathematics》1981,33(1):135-140
Summary LetF be a distribution function over the real line. DefineR
p(y)=∫|x−y|pdF(x) forp≧1. Forp>1 there is a unique minimizer ofR
p(·), sayγ
p. Under mild conditions onF it is shown that
exists and that the limit is a median. Thus, one could use this limit as a definition of a unique median. Also it is shown
that
whereR is the right extremity ofF andL is the left extremity ofF provided that −∞<L≦R<∞. A similar result is available ifL=−∞,R=∞, yetF has symmetric tails. 相似文献
18.
LU Chuanrong QIU Jin & XU Jianjun School of Mathematics Statistics Zhejiang University of Finance Economics Hangzhou China Department of Mathematics Zhejiang University Hangzhou China 《中国科学A辑(英文版)》2006,49(12):1788-1799
Let {Xn,-∞< n <∞} be a sequence of independent identically distributed random variables with EX1 = 0, EX12 = 1 and let Sn =∑k=1∞Xk, and Tn = Tn(X1,…,Xn) be a random function such that Tn = ASn Rn, where supn E|Rn| <∞and Rn = o(n~(1/2)) a.s., or Rn = O(n1/2-2γ) a.s., 0 <γ< 1/8. In this paper, we prove the almost sure central limit theorem (ASCLT) and the function-typed almost sure central limit theorem (FASCLT) for the random function Tn. As a consequence, it can be shown that ASCLT and FASCLT also hold for U-statistics, Von-Mises statistics, linear processes, moving average processes, error variance estimates in linear models, power sums, product-limit estimators of a continuous distribution, product-limit estimators of a quantile function, etc. 相似文献
19.
Quanhua Xu 《Israel Journal of Mathematics》1995,91(1-3):173-187
Let (Ω,F, P) be a probability space and {F
n}n≥0 a regular increasing sequence of sub-σ-fields ofF. LetH
1(Ω) be the usual Hardy space ofF
n-martingales. We show that the couple (H
1(Ω),L
∞(Ω)) is a partial retract of (L
1(Ω),L
∞(Ω)). It is also proved that (L
p(Ω),BMO(Ω)) is a partial retract of (L
p(Ω),L
∞(Ω)) for all 1<p<∞. 相似文献
20.
Charles Horowitz 《Israel Journal of Mathematics》1978,30(3):285-291
LesB denote the class of functions analytic in the unit disc ofC which satisfy 0<|f(z)|<1. It is proved that there exists a numberc<1 such that iff∈B and iff(z)=Σ
n=0
∞
a
n
z
n
, then |a
n
|<c forn>=1. 相似文献