共查询到20条相似文献,搜索用时 203 毫秒
1.
A. I. Martikainen 《Journal of Mathematical Sciences》2006,133(3):1308-1313
Let {Xi, Yi}i=1,2,... be an i.i.d. sequence of bivariate random vectors with P(Y1 = y) = 0 for all y. Put Mn(j) = max0≤k≤n-j (Xk+1 + ... Xk+j)Ik,j, where Ik,k+j = I{Yk+1 < ⋯ < Yk+j} denotes the indicator function for the event in brackets, 1 ≤ j ≤ n. Let Ln be the largest index l ≤ n for which Ik,k+l = 1 for some k = 0, 1, ..., n - l. The strong law of large numbers for “the maximal gain over the longest increasing runs,”
i.e., for Mn(Ln) has been recently derived for the case where X1 has a finite moment of order 3 + ε, ε > 0. Assuming that X1 has a finite mean, we prove for any a = 0, 1, ..., that the s.l.l.n. for M(Ln - a) is equivalent to EX
1
3+a
I{X1 > 0} < ∞. We derive also some new results for the a.s. asymptotics of Ln. Bibliography: 5 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 311, 2004, pp. 179–189. 相似文献
2.
L. V. Rozovsky 《Journal of Mathematical Sciences》2010,167(4):543-549
We study logarithmic small deviations of
M = supj \geqslant 1 ljXj M = \mathop {\sup }\limits_{j \geqslant 1} {\lambda_j}{X_j} , where {X
j
} are i.i.d. nonnegative random variables and {λ
j
} is a sequence of positive nonincreasing numbers that satisfies certain conditions of regularity. Bibliography: 3 titles. 相似文献
3.
L. V. Rozovsky 《Journal of Mathematical Sciences》2007,147(4):6935-6945
In this note, we give estimates of small deviation probabilities of the sum ∑j≥1 λj Xj, where {λj} are nonnegative numbers and {Xj} are i.i.d. positive random variables that satisfy mild assumptions at zero and infinity. Bibliography: 10 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 341, 2007, pp. 151–167. 相似文献
4.
Let B be an unbounded domain located outside an angle domain with vertex at the origin, A ={λn}(n = 1,2,...) be a sequence of complex numbers satisfying sup | arg(λn)| 〈 α 〈 π/2 and denote by M(∧) = {z^λ, λ ∈ ∧} the corresponding system of functions z^λ(λ∈∧). Let α0(z) be a weight function defined on B. We obtain a completeness theorem for the system M(∧) in the Hilbert space L^2 [B, α0]. 相似文献
5.
For κ ⩾ 0 and r0 > 0 let ℳ(n, κ, r0) be the set of all connected, compact n-dimensional Riemannian manifolds (Mn, g) with Ricci (M, g) ⩾ −(n−1) κ g and Inj (M) ⩾ r0. We study the relation between the kth eigenvalue λk(M) of the Laplacian associated to (Mn,g), Δ = −div(grad), and the kth eigenvalue λk(X) of a combinatorial Laplacian associated to a discretization X of M. We show that there exist constants c, C > 0 (depending only on n, κ and r0) such that for all M ∈ ℳ(n, κ, r0) and X a discretization of
for all k < |X|. Then, we obtain the same kind of result for two compact manifolds M and N ∈ ℳ(n, κ, r0) such that the Gromov–Hausdorff distance between M and N is smaller than some η > 0. We show that there exist constants c, C > 0 depending on η, n, κ and r0 such that
for all
.
Mathematics Subject Classification (2000): 58J50, 53C20
Supported by Swiss National Science Foundation, grant No. 20-101 469 相似文献
6.
J. Sunklodas 《Lithuanian Mathematical Journal》2005,45(4):475-486
We derive a lower bound of L
p
norms, 1 ⩽ p ⩽ ∞, in the central limit theorem for strongly mixing random variables X
1,..., X
n
with
under the boundedness condition ℙ{|X
i
| ⩽ M} = 1 with a nonrandom constantM > 0 and condition ∑
r⩾1
r
2α(r) < ∞, where α(r) are the Rosenblatt strong mixing coefficients.
__________
Translated from Lietuvos Matematikos Rinkinys, Vol. 45, No. 4, pp. 587–602, October–December, 2005. 相似文献
7.
Ruan Huojun Dai Meifeng Su Weiyi Dept. of Math. Zhejiang Univ. Hangzhou China. Dept. of Math. Jiangsu Univ. Zhenjiang China. Dept. of Math. Nanjing Univ. Nanjing China. 《高校应用数学学报(英文版)》2005,20(2):235-242
§ 1 IntroductionThe class of Cantor sets is a typical one of sets in fractal geometry.Mathematicianshave paid their attentions to such sets for a long time.Itis well known that the Hausdorffmeasure of the Cantor middle- third set is1(see[1]) .Recently,Feng[3] obtained the exactvalues of the packing measure for a class of linear Cantor sets.Using Feng s method,Zhuand Zhou[5] obtained the exactvalue of Hausdorff centred measure of the symmetry Cantorsets.In this papar,we consider the Ha… 相似文献
8.
Abstract
Let Λ = {λ
k
} be an infinite increasing sequence of positive integers with λ
k
→∞. Let X = {X(t), t ∈? R
N
} be a multi-parameter fractional Brownian motion of index α(0 < α < 1) in R
d
. Subject to certain hypotheses, we prove that if N < αd, then there exist positive finite constants K
1 and K
2 such that, with unit probability,
if and only if there exists γ > 0 such that
where ϕ(s) = s
N/α
(log log 1/s)
N/(2α), ϕ-p
Λ(E) is the Packing-type measure of E,X([0, 1])
N
is the image and GrX([0, 1]
N
) = {(t,X(t)); ∈? [0, 1]
N
} is the graph of X, respectively. We also establish liminf type laws of the iterated logarithm for the sojourn measure of X.
Supported by the National Natural Science Foundation of China (No.10471148), Sci-tech Innovation Item for Excellent Young
and Middle-Aged University Teachers and Major Item of Educational Department of Hubei (No.2003A005) 相似文献
9.
Onur Yavuz 《Integral Equations and Operator Theory》2007,58(3):433-446
We consider a multiply connected domain
where
denotes the unit disk and
denotes the closed disk centered at
with radius r
j
for j = 1, . . . , n. We show that if T is a bounded linear operator on a Banach space X whose spectrum contains ∂Ω and does not contain the points λ1, λ2, . . . , λ
n
, and the operators T and r
j
(T − λ
j
I)−1 are polynomially bounded, then there exists a nontrivial common invariant subspace for T
* and (T − λ
j
I)*-1. 相似文献
10.
Yossi Moshe 《Journal d'Analyse Mathématique》2006,99(1):267-294
Let λ be the upper Lyapunov exponent corresponding to a product of i.i.d. randomm×m matrices (X
i)
i
0/∞
over ℂ. Assume that theX
i's are chosen from a finite set {D
0,D
1...,D
t-1(ℂ), withP(X
i=Dj)>0, and that the monoid generated byD
0, D1,…, Dq−1 contains a matrix of rank 1. We obtain an explicit formula for λ as a sum of a convergent series. We also consider the case
where theX
i's are chosen according to a Markov process and thus generalize a result of Lima and Rahibe [22].
Our results on λ enable us to provide an approximation for the numberN
≠0(F(x)n,r) of nonzero coefficients inF(x)
n.(modr), whereF(x) ∈ ℤ[x] andr≥2. We prove the existence of and supply a formula for a constant α (<1) such thatN
≠0(F(x)n,r) ≈n
α for “almost” everyn.
Supported in part by FWF Project P16004-N05 相似文献
11.
Fu Qing GAO 《数学学报(英文版)》2007,23(8):1527-1536
Let {Xn;n≥ 1} be a sequence of independent non-negative random variables with common distribution function F having extended regularly varying tail and finite mean μ = E(X1) and let {N(t); t ≥0} be a random process taking non-negative integer values with finite mean λ(t) = E(N(t)) and independent of {Xn; n ≥1}. In this paper, asymptotic expressions of P((X1 +… +XN(t)) -λ(t)μ 〉 x) uniformly for x ∈[γb(t), ∞) are obtained, where γ〉 0 and b(t) can be taken to be a positive function with limt→∞ b(t)/λ(t) = 0. 相似文献
12.
Let M(σ) = sup{|F(σ + it)|: t ∈ ℝ} and μ(σ) = max {|a
n
|exp(σλn): n ≥ 0}, σ < 0, for a Dirichlet series {fx995-01} with abscissa of absolute convergence σa = 0. We prove that the condition ln ln n = o(ln λn), n → ∞, is necessary and sufficient for the equivalence of the relations {fx995-02}, for each series of this type.
Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 6, pp. 851–856, June, 2008. 相似文献
13.
Simeon M. Berman 《Annals of the Institute of Statistical Mathematics》1984,36(1):301-321
Summary Let {X
n,j,−∞<j<∞∼,n≧1, be a sequence of stationary sequences on some probability space, with nonnegative random variables. Under appropriate
mixing conditions, it is shown thatS
n=Xn,1+…+X
n,n has a limiting distribution of a general infinitely divisible form. The result is applied to sequences of functions {f
n(x)∼ defined on a stationary sequence {X
j∼, whereX
n.f=fn(Xj). The results are illustrated by applications to Gaussian processes, Markov processes and some autoregressive processes of
a general type.
This paper represents results obtained at the Courant Institute of Mathematical Sciences, New York University, under the sponsorship
of the National Sciences Foundation, Grant MCS 82-01119. 相似文献
14.
In this paper, we consider the following Reinhardt domains. Let M = (M1, M2,..., Mn) : [0,1] → [0,1]^n be a C2-function and Mj(0) = 0, Mj(1) = 1, Mj″ 〉 0, C1jr^pj-1 〈 Mj′(r) 〈 C2jr^pj-1, r∈ (0, 1), pj 〉 2, 1 ≤ j ≤ n, 0 〈 C1j 〈 C2j be constants. Define
DM={z=(z1,z2,…,Zn)^T∈C^n:n∑j=1 Mj(|zj|)〈1}
Then DM C^n is a convex Reinhardt domain. We give an extension theorem for a normalized biholomorphic convex mapping f : DM -→ C^n. 相似文献
DM={z=(z1,z2,…,Zn)^T∈C^n:n∑j=1 Mj(|zj|)〈1}
Then DM C^n is a convex Reinhardt domain. We give an extension theorem for a normalized biholomorphic convex mapping f : DM -→ C^n. 相似文献
15.
Brice Franke 《Extremes》2011,14(1):127-152
We investigate the recursive sequence Z
n
: = max {Z
n − 1,λ(Z
n − 1)X
n
} where X
n
is a sequence of iid random variables with exponential distributions and λ is a periodic positive bounded measurable function. We prove that the Césaro mean of the sequence λ(Z
n
) converges toward the essential minimum of λ. Subsequently we apply this result and obtain a limit theorem for the distributions of the sequence Z
n
. The resulting limit is a Gumbel distribution. 相似文献
16.
André Adler 《Central European Journal of Mathematics》2006,4(1):1-4
Consider independent and identically distributed random variables {X
nk, 1 ≤ k ≤ m, n ≤ 1} from the Pareto distribution. We select two order statistics from each row, X
n(i) ≤ X
n(j), for 1 ≤ i < j ≤ = m. Then we test to see whether or not Laws of Large Numbers with nonzero limits exist for weighted sums of the random variables
R
ij = X
n(j)/X
n(i). 相似文献
17.
R. E. Maiboroda 《Ukrainian Mathematical Journal》1998,50(7):1067-1079
For a process X(t)=Σ
j=1
M
g
j
(t)ξ
j
(), where gj(t) are nonrandom given functions, is a stationary vector-valued Gaussian process, Eξk(t) = 0, and Eξk(0) Eξl(τ) = r
kl(τ), we construct an estimate for the functions r
kl(τ) on the basis of observations X(t), t ∈ [0, T]. We establish conditions for the asymptotic normality of as T → ∞. We consider the problem of the optimal choice of parameters of the estimate depending on observations.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 7, pp. 937–947, July, 1998. 相似文献
18.
An optimal bound on the tail distribution of the number of recurrences of an event in product spaces
Let X
1
,X
2
,... be independent random variables and a a positive real number. For the sake of illustration, suppose A is the event that |X
i+1
+...+X
j
|≥a for some integers 0≤i<j<∞. For each k≥2 we upper-bound the probability that A occurs k or more times, i.e. that A occurs on k or more disjoint intervals, in terms of P(A), the probability that A occurs at least once.
More generally, let X=(X
1
,X
2
,...)Ω=Π
j
≥1Ω
j
be a random element in a product probability space (Ω,ℬ,P=⊗
j
≥1
P
j
). We are interested in events AB that are (at most contable) unions of finite-dimensional cylinders. We term such sets sequentially searchable. Let L(A) denote the (random) number of disjoint intervals (i,j] such that the value of X
(i,j]
=(X
i+1
,...,X
j
) ensures that XA. By definition, for sequentially searchable A, P(A)≡P(L(A)≥1)=P(𝒩−ln
(P(Ac))
≥1), where 𝒩γ denotes a Poisson random variable with some parameter γ>0. Without further assumptions we prove that, if 0<P(A)<1, then P(L(A)≥k)<P(𝒩−ln
(P(Ac))
≥k) for all integers k≥2.
An application to sums of independent Banach space random elements in l
∞
is given showing how to extend our theorem to situations having dependent components.
Received: 8 June 2001 / Revised version: 30 October 2002 Published online: 15 April 2003
RID="*"
ID="*" Supported by NSF Grant DMS-99-72417.
RID="†"
ID="†" Supported by the Swedish Research Council.
Mathematics Subject Classification (2000): Primary 60E15, 60G50
Key words or phrases: Tail probability inequalities – Hoffmann-Jo rgensen inequality – Poisson bounds – Number of event recurrences – Number of
entrance times – Product spaces 相似文献
19.
In this paper we give necessary and sufficient conditions for the block sequence of the set X = {x
1 < x
2 < … < x
n
< …} ⊂ ℕ to have an asymptotic distribution function in the form x
λ. 相似文献
20.
Onur Yavuz 《Integral Equations and Operator Theory》2010,68(4):473-485
We consider a multiply connected domain Ω which is obtained by removing n closed disks which are centered at λ
j
with radius r
j
for j = 1, . . . , n from the unit disk. We assume that T is a bounded linear operator on a separable reflexive Banach space whose spectrum contains ∂Ω and does not contain the points
λ1, λ2, . . . , λ
n
, and the operators T and r
j
(T − λ
j
I)−1 are polynomially bounded. Then either T has a nontrivial hyperinvariant subspace or the WOT-closure of the algebra {f(T) : f is a rational function with poles off [`(W)]{\overline\Omega}} is reflexive. 相似文献