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1.
For an array {V
nk
,k1,n1} of rowwise independent random elements in a real separable Banach space
with almost surely convergent row sums
, we provide criteria for S
n
–A
n
to be stochastically bounded or for the weak law of large numbers
to hold where {A
n
,n1} is a (nonrandom) sequence in
. 相似文献
2.
Define
, where
is a symmetric U-type statistic, H
k() is the Hermite polynomial of degree k, and {X, X
n, n1} are independent identically distributed binary random variables with Pr(X{–1, 1}})=1. We show that
according as EX=0 or EX0, respectively. 相似文献
3.
Chang Jen-Chun Chen Rong-Jaye Hwang Frank K. 《Methodology and Computing in Applied Probability》2001,3(4):379-386
A d-within-consecutive-k-out-of-n system, abbreviated as Con(d, k, n), is a linear system of n components in a line which fails if and only if there exists a set of k consecutive components containing at least d failed ones. So far the fastest algorithm to compute the reliability of Con(d, k, n) is Hwang and Wright's
algorithm published in 1997, where
. In this paper we use automata theory to reduce
to
. For d small or close to k, we have reduced
from exponentially many (in k) to polynomially many. The computational complexity of our final algorithm is
, where
. 相似文献
4.
Let
be i.i.d. random variables and let, for each
and
. It is shown that
a.s. whenever the sequence of self-normalized sums S
n
/V
n is stochastically bounded, and that this limsup is a.s. positive if, in addition, X is in the Feller class. It is also shown that, for X in the Feller class, the sequence of self-normalized sums is stochastically bounded if and only if
相似文献
5.
Florence Merlevède Magda Peligrad Sergey Utev 《Journal of Theoretical Probability》1997,10(3):681-693
In this paper we study the behavior of sums of a linear process
associated to a strictly stationary sequence
with values in a real separable Hilbert space and
are linear operators from H to H. One of the results is that
satisfies the CLT provided
are i.i.d. centered having finite second moments and
. We shall provide an example which shows that the condition on the operators is essentially sharp. Extensions of this result are given for sequences of weak dependent random variables
under minimal conditions. 相似文献
6.
Let u(x) xR
q
be a symmetric nonnegative definite function which is bounded outside of all neighborhoods of zero but which may have u(0)=. Let p
x, (·) be the density of an R
q
valued canonical normal random variable with mean x and variance and let {G
x, ; (x, )R
q
×[0,1 ]} be the mean zero Gaussian process with covariance
A finite positive measure on R
q
is said to be in
with respect to u, if
When
, a multiple Wick product chaos
is defined to be the limit in L
2, as 0, of
where
,
denotes the Wick product of the m
j
normal random variables
.Consider also the associated decoupled chaos processes
,
defined as the limit in L
2, as 0, of
where
are independent copies of G
x,.Define
Note that a neighborhood of the diagonals of
in
is excluded, except those points on the diagonal which originate in the same Wick product in (i). Set
One of the main results of this paper is:
Theorem A. If
is continuous on (R
q
)
r
for all
then
is continuous on
.When u satisfies some regularity conditions simple sufficient conditions are obtained for the continuity of
on (R
q
)
r
. Also several variants of (i) are considered and related to different types of decoupled processes. These results have applications in the study of intersections of Lévy process and continuous additive functionals of several Lévy processes. 相似文献
7.
Let
be a continuous semimartingale and let
be a continuous function of bounded variation. Setting
and
suppose that a continuous function
is given such that F is C1,2 on
and F is
on
. Then the following change-of-variable formula holds:
where
is the local time of X at the curve b given by
and
refers to the integration with respect to
. A version of the same formula derived for an Itô diffusion X under weaker conditions on F has found applications in free-boundary problems of optimal stopping. 相似文献
8.
Noboru Hamada 《Designs, Codes and Cryptography》1997,10(1):41-56
Let k and d be any integers such that k 4 and
. Then there exist two integers and in {0,1,2} such that
. The purpose of this paper is to prove that (1) in the case k 5 and (,) = (0,1), there exists a ternary
code meeting the Griesmer bound if and only if
and (2) in the case k 4 and (,) = (0,2) or (1,1), there is no ternary
code meeting the Griesmer bound for any integers k and d and (3) in the case k 5 and
, there is no projective ternary
code for any integers k and such that 1k-3, where
and
for any integer i 0. In the special case k=6, it follows from (1) that there is no ternary linear code with parameters [233,6,154] , [234,6,155] or [237,6,157] which are new results. 相似文献
9.
Let (X
t
) be a one dimensional diffusion corresponding to the operator
, starting from x>0 and T
0 be the hitting time of 0. Consider the family of positive solutions of the equation
with (0, ), where
. We show that the distribution of the h-process induced by any such is
, for a suitable sequence of stopping times (S
M
: M0) related to which converges to with M. We also give analytical conditions for
, where
is the smallest point of increase of the spectral measure associated to
. 相似文献
10.
Let
be an
-filtered category in the sense of Karoubi. This is the categorical analogue of an ideal
in a ring
. Pedersen and Weibel constructed a fibration of K-theory spectra associated with the sequence
. We present a new easier proof based on Waldhausen' generic fibration. 相似文献
11.
We construct a metric space of set functions (
, d) such that a sequence {P
n} of Borel probability measures on a metric space (
, d*) satisfies the full Large Deviation Principle (LDP) with speed {a
n} and good rate function I if and only if the sequence
converges in (
, d) to the set function e
–I
. Weak convergence of probability measures is another special case of convergence in (
, d). Properties related to the LDP and to weak convergence are then characterized in terms of (
, d). 相似文献
12.
Let {S
n}
n0 be a random walk on the line. We give criteria for the existence of a nonrandom sequence n
i for which
respectively
We thereby obtain conditions for to be a strong limit point of {S
n} or {S
n
/n}. The first of these properties is shown to be equivalent to
for some sequence a
i , where T(a) is the exit time from the interval [–a,a]. We also obtain a general equivalence between
and
for an increasing function fand suitable sequences n
i and a
i. These sorts of properties are of interest in sequential analysis. Known conditions for
and
(divergence through the whole sequence n) are also simplified. 相似文献
13.
On the Harris Recurrence of Iterated Random Lipschitz Functions and Related Convergence Rate Results 总被引:1,自引:0,他引:1
Gerold Alsmeyer 《Journal of Theoretical Probability》2003,16(1):217-247
A result by Elton(6) states that an iterated function system
of i.i.d. random Lipschitz maps F
1,F
2,... on a locally compact, complete separable metric space
converges weakly to its unique stationary distribution if the pertinent Liapunov exponent is a.s. negative and
for some
. Diaconis and Freedman(5) showed the convergence rate be geometric in the Prokhorov metric if
for some p>0, where L
1 denotes the Lipschitz constant of F
1. The same and also polynomial rates have been recently obtained in Alsmeyer and Fuh(1) by different methods. In this article, necessary and sufficient conditions are given for the positive Harris recurrence of (M
n
)
n0 on some absorbing subset
. If
and the support of has nonempty interior, we further show that the same respective moment conditions ensuring the weak convergence rate results mentioned above now lead to polynomial, respectively geometric rate results for the convergence to in total variation or f-norm
f
, f(x)=1+d(x,x
0)
for some (0,p]. The results are applied to various examples that have been discussed in the literature, including the Beta walk, multivariate ARMA models and matrix recursions. 相似文献
14.
In this paper, we consider equations of the form
, where
is a function with values in the Hilbert space
, the operator B is symmetric, and the operator A is uniformly positive and self-adjoint in
. The linear operator
generating the C
0-semigroup in the energy space
is associated with this equation. We prove that this semigroup is exponentially stable if the operator B is uniformly positive and the operator A dominates B in the sense of quadratic forms. 相似文献
15.
Avishay Vaknin 《K-Theory》2001,24(1):57-68
For a small triangulated category
, Bass's K
1 group
is described, and the theorem of the heart is proved. We define the determinant map from
to Neeman's
, and we compute this map when
is the derived category of an Abelian category
. 相似文献
16.
N. Guillotin-Plantard 《Journal of Theoretical Probability》2001,14(1):241-260
In this paper, we study a
d
-random walk
on nearest neighbours with transition probabilities generated by a dynamical system
. We prove, at first, that under some hypotheses,
verifies a local limit theorem. Then, we study these walks in a random scenery
, a sequence of independent, identically distributed and centred random variables and show that for certain dynamic random walks,
satisfies a strong law of large numbers. 相似文献
17.
Aderemi Kuku 《K-Theory》2001,22(4):367-392
Let
be a rational prime,
an exact category. In this article, we define and study for all
, the profinite higher K-theory of
, that is
as well as
, where
is the
-dimensional mod-
Moore space. We study connections between
and prove several
-completeness results involving these and associated groups including the cases where
is the category of finitely generated (resp. finitely generated projective) modules over orders in semi-simple algebras over number fields and p-adic fields. We also define and study continuous K-theory
of orders in p-adic semi-simple algebras and show some connection between the profinite and continuous K-theory of . 相似文献
18.
Real valued M-estimators
in a statistical model 1 with observations
are replaced by
-valued M-estimators
in a new model with observations
where
are regressors,
is a structural parameter and
a structural function of the new model. Sufficient conditions for the consistency of
are derived, motivated by the sufficiency conditions for the simpler parent estimator
The result is a general method of consistent estimation in a class of nonlinear (pseudolinear) statistical problems. If F
has a natural exponential density ex–b( x ) then our pseudolinear model with u = (g o )–1 reduces to the well known generalized linear model, provided () = db()/d and g is the so-called link function of the generalized linear model. General results are illustrated for special pairs and leading to some classical M-estimators of mathematical statistics, as well as to a new class of generalized -quantile estimators. 相似文献
19.
Ján Jakubík 《Czechoslovak Mathematical Journal》2002,52(3):651-663
Let Int
be the lattice of all intervals of an MV-algebra
. In the present paper we investigate the relations between direct product decompositions of
and (i) the lattice Int
, or (ii) 2-periodic isometries on
, respectively. 相似文献
20.
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