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1.
Precise Asymptotics in the Law of the Iterated Logarithm of Moving-Average Processes 总被引:1,自引:0,他引:1
Yun Xia LI Li Xin ZHANG 《数学学报(英文版)》2006,22(1):143-156
In this paper, we discuss the moving-average process Xk = ∑i=-∞ ^∞ ai+kεi, where {εi;-∞ 〈 i 〈 ∞} is a doubly infinite sequence of identically distributed ψ-mixing or negatively associated random variables with mean zeros and finite variances, {ai;-∞ 〈 i 〈 -∞) is an absolutely solutely summable sequence of real numbers. 相似文献
2.
A general result on precise asymptotics for linear processes of positively associated sequences 总被引:2,自引:0,他引:2
Let {εt; t ∈ Z^+} be a strictly stationary sequence of associated random variables with mean zeros, let 0〈Eε1^2〈∞ and σ^2=Eε1^2+1∑j=2^∞ Eε1εj with 0〈σ^2〈∞.{aj;j∈Z^+} is a sequence of real numbers satisfying ∑j=0^∞|aj|〈∞.Define a linear process Xt=∑j=0^∞ ajεt-j,t≥1,and Sn=∑t=1^n Xt,n≥1.Assume that E|ε1|^2+δ′〈 for some δ′〉0 and μ(n)=O(n^-ρ) for some ρ〉0.This paper achieves a general law of precise asymptotics for {Sn}. 相似文献
3.
H. Teicher 《Probability Theory and Related Fields》1988,79(2):303-316
Summary If
where {X
n j
,ℱ
n j
1≦j≦m
n
↑∞, n≧1} is a martingale difference array, conditions are given for the distribution and moment convergence of S
n,k
to the distribution and moments of
where H
k
is the Hermite polynomial of degree k and Z is a standard normal variable. This is intimately related to an identity (*) for multiple Wiener integrals. Under alternative
conditions, similar results hold for S
n, k
/U
n
k
and S
n, k
/V
n
k
where
and V
n
2
V
n
2
is the conditional variance.
Research supported by the National Science Foundation under Grant DMS-8601346 相似文献
4.
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
5.
We analyze polynomials P
n
that are biorthogonal to exponentials
, in the sense that
Here α>−1. We show that the zero distribution of P
n
as n→∞ is closely related to that of the associated exponent polynomial
More precisely, we show that the zero counting measures of {P
n
(−4nx)}
n=1∞ converge weakly if and only if the zero counting measures of {Q
n
}
n=1∞ converge weakly. A key step is relating the zero distribution of such a polynomial to that of the composite polynomial
under appropriate assumptions on {Δ
n,j
}.
相似文献
6.
S. Norvidas 《Lithuanian Mathematical Journal》2009,49(2):185-189
For a compact set K in ℝ
n
, let B
2
K
be the set of all functions f ∈ L
2(ℝ2) bandlimited to K, i.e., such that the Fourier transform f̂ of f is supported by K. We investigate the question of approximation of f ∈ B
2
K
by finite exponential sums
in the space , as τ → ∞. 相似文献
7.
Consider the parameter space Θ which is an open subset of ℝ
k
,k≧1, and for each θ∈Θ, let the r.v.′sY
n
,n=0, 1, ... be defined on the probability space (X,A,P
θ) and take values in a Borel setS of a Euclidean space. It is assumed that the process {Y
n
},n≧0, is Markovian satisfying certain suitable regularity conditions. For eachn≧1, let υ
n
be a stopping time defined on this process and have some desirable properties. For 0 < τ
n
→ ∞ asn→∞, set
h
n
→h ∈R
k
, and consider the log-likelihood function
of the probability measure
with respect to the probability measure
. Here
is the restriction ofP
θ to the σ-field induced by the r.v.′sY
0,Y
1, ...,
. The main purpose of this paper is to obtain an asymptotic expansion of
in the probability sense. The asymptotic distribution of
, as well as that of another r.v. closely related to it, is obtained under both
and
.
This research was supported by the National Science Foundation, Grant MCS77-09574.
Research supported by the National Science Foundation, Grant MCS76-11620. 相似文献
8.
Precise Rates in the Law of Iterated Logarithm for the Moment of I.I.D. Random Variables 总被引:1,自引:0,他引:1
Ye JIANG Li Xin ZHANG 《数学学报(英文版)》2006,22(3):781-792
Let{X,Xn;n≥1} be a sequence of i,i.d, random variables, E X = 0, E X^2 = σ^2 〈 ∞.Set Sn=X1+X2+…+Xn,Mn=max k≤n│Sk│,n≥1.Let an=O(1/loglogn).In this paper,we prove that,for b〉-1,lim ε→0 →^2(b+1)∑n=1^∞ (loglogn)^b/nlogn n^1/2 E{Mn-σ(ε+an)√2nloglogn}+σ2^-b/(b+1)(2b+3)E│N│^2b+3∑k=0^∞ (-1)k/(2k+1)^2b+3 holds if and only if EX=0 and EX^2=σ^2〈∞. 相似文献
9.
Narcisse Randrianantoanina 《Israel Journal of Mathematics》2004,140(1):333-365
We prove a non-commutative version of the weak-type (1,1) boundedness of square functions of martingales. More precisely,
we prove that there is an absolute constantK with the following property: ifM is a semifinite von Neumann algebra with a faithful normal traceτ and (M
n
)
n=1
∞
is an increasing filtration of von Neumann subalgebras of (M then for any martingalex=
n=1
∞
inL
1(M,τ), adapted to (M
n
)
n=1
∞
, there is a decomposition into two sequences (x
n
)
n=1
∞
and (z
n
)
n=1
∞
withx
n=y
n+z
nfor everyn≥1 and such that
. This generalizes a result of Burkholder from classical martingale theory to non-commutative martingales. We also include
some applications to martingale Hardy spaces.
Supported in part by NSF grant DMS-0096696. 相似文献
10.
J. Sunklodas 《Lithuanian Mathematical Journal》2007,47(3):327-335
We estimate the difference
for bounded functions h: ℝ → ℝ satisfying the Lipschitz condition, where Z
v
= B
v
−1
∑
i=0
∞
v
i
X
i
and
with discount factor ν such that 0 < ν < 1. Here {X
n
, n ≥ 0} is a sequence of strongly mixing random variables with
, and N is a standard normal random variable. In a particular case, the obtained upper bounds are of order O((1 − ν)1/2).
Published in Lietuvos Matematikos Rinkinys, Vol. 47, No. 3, pp. 399–409, July–September, 2007.
The research was partially supported by the Lithuanian State Science and Studies Foundation, grant No. T-15/07. 相似文献
11.
Y. K. Belyaev 《Journal of Mathematical Sciences》1996,81(5):2888-2893
Let the statistical data be a collection of n piecesx
1, ...,x
n of simple renewal processes. The random times between renewals have an unknown cumulative hazard function (c.h.f.) H0(·). Let τ(H(·)) be the value of some functional τ(·), given c.h.f. H(·). The value τ0=τ(H0(·)) is a parameter of interest. If
is an estimator for τ0, then its quality can be characterized by the distribution law of normed deviations
. These laws Ln are unknown, but they can be consistently estimated, by using the resampling method, as n→∞. In the case considered, the
resampling method can be justified as a special case of the central limit resampling theorem.
Supported by the Bank of Sweden Tercentenary Foundation.
Proceedings of the XVII Seminar on Stability Problems for Stochastic Models, Kazan, Russia, 1995, Part I. 相似文献
12.
Isaac Meilijson 《Israel Journal of Mathematics》1973,15(2):193-203
The behavior of (1/N)
asN→∞ is considered, wheref is a bounded measurable function on (−∞, ∞) and (S
n)
n
=1/∞
are the partial sums of a sequence of independent and identically distributed rondom variables. 相似文献
13.
We prove that if u
1,u
2:(0,∞)×ℝ
d
→(0,∞) are sufficiently well-behaved solutions to certain heat inequalities on ℝ
d
then the function u:(0,∞)×ℝ
d
→(0,∞) given by
also satisfies a heat inequality of a similar type provided
. On iterating, this result leads to an analogous statement concerning n-fold convolutions. As a corollary, we give a direct heat-flow proof of the sharp n-fold Young convolution inequality and its reverse form.
Both authors were supported by EPSRC grant EP/E022340/1. 相似文献
14.
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
15.
Frank Blume 《Israel Journal of Mathematics》1998,108(1):1-12
If (X,T) is a completely ergodic system, then there exists a positive monotone increasing sequence {a
n
}
n
1/∞
with lim
n
→∞a
n
=∞ and a positive concave functiong defined on [1, ∞) for whichg(x)/x
2 isnot integrable such that
for all nontrivial partitions α ofX into two sets. 相似文献
16.
周泽华 《中国科学A辑(英文版)》2003,46(1):33-38
Let Un be the unit polydisc of Cn and φ= (φ1,...,φn? a holomorphic self-map of Un. Let 0≤α< 1. This paper shows that the composition operator Cφ, is bounded on the Lipschitz space Lipa(Un) if and only if there exists M > 0 such thatfor z∈Un. Moreover Cφ is compact on Lipa(Un) if and only if Cφ is bounded on Lipa(Un) and for every ε > 0, there exists a δ > 0 such that whenever dist(φ(z),σUn) <δ 相似文献
17.
A. V. Harutyunyan W. Lusky 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2010,45(3):128-135
Let U
n
be the unit polydisk in C
n
and S be the space of functions of regular variation. Let 1 ≤ p < ∞, ω = (ω
1, ..., ω
n
), ω
j
∈ S(1 ≤ j ≤ n) and f ∈ H(U
n
). The function f is said to be in holomorphic Besov space B
p
(ω) if
$
\left\| f \right\|_{B_p (\omega )}^p = \int_{U^n } {\left| {Df(z)} \right|^p \prod\limits_{j = 1}^n {\frac{{\omega _j (1 - |z_j |)}}
{{(1 - |z_j |^{2 - p} )}}} dm_{2n} (z) < + \infty }
$
\left\| f \right\|_{B_p (\omega )}^p = \int_{U^n } {\left| {Df(z)} \right|^p \prod\limits_{j = 1}^n {\frac{{\omega _j (1 - |z_j |)}}
{{(1 - |z_j |^{2 - p} )}}} dm_{2n} (z) < + \infty }
相似文献
18.
Lars Schäfer 《Annals of Global Analysis and Geometry》2007,32(2):125-145
In this paper we study para-tt *-bundles (TM, D, S) on the tangent bundle of an almost para-complex manifold (M, τ). We characterise those para-tt *-bundles with ${\nabla=D + S}
19.
I. Kiguradze 《Georgian Mathematical Journal》1994,1(5):487-494
The properties of solutions of the equationu″(t) =p
1(t)u(τ1(t)) +p
2(t)u′(τ2(t)) are investigated wherep
i
:a, + ∞[→R (i=1,2) are locally summable functions τ1 :a, + ∞[→R is a measurable function, and τ2 :a, + ∞[→R is a nondecreasing locally absolutely continuous function. Moreover, τ
i
(t) ≥t (i = 1,2),p
1(t)≥0,p
2
2
(t) ≤ (4 - ɛ)τ
2
′
(t)p
1(t), ɛ =const > 0 and
. In particular, it is proved that solutions whose derivatives are square integrable on [α,+∞] form a one-dimensional linear
space and for any such solution to vanish at infinity it is necessary and sufficient that
. 相似文献
20.
S. P. Eveson 《Integral Equations and Operator Theory》2005,53(3):331-341
Given k ∈ L1 (0,1) satisfying certain smoothness and growth conditions at 0, we consider the Volterra convolution operator Vk defined on Lp (0,1) by
|