共查询到20条相似文献,搜索用时 46 毫秒
1.
FUBINITHEOREMw.r.t.STOCHASTICMEASUREONPRODUCTMEASURABLESPACECHENPEIDE(陈培德)(InstituteofAppliedMathematics,theChineseAcademyofS... 相似文献
2.
Qiguang Wu 《应用数学学报(英文版)》1993,9(3):281-288
LetY be distributed according to ann-variate normal distribution with a meanX and a nonsingular covariance matrix
2
V, where bothX andV are known, R
p
is a parameter, > 0 is known or unknown. Denote
and
. Assume thatF is linearly estimable. When is known, it is proved that the unbiased loss estimator
2tr(F(XV
–1
X)–
F) of
is admissible for rank (F)=k4 and inadmissible fork 5 with the squared error loss
. When is unknown and rank (X) <n, it is established that the loss estimatorcS
2, wherec is any nonnegative constant, of
is inadmissible and that the unbiased loss estimator tr(F(XV
–1
X)–
F) of
is admissible fork 4, and inadmissible fork 5 with squared error loss.This project is supported by the National Natural Science Foundation of China. 相似文献
3.
Gerd Herzog 《Periodica Mathematica Hungarica》1995,30(3):205-210
Given a sequence (
n
)
n
in
with
there are functions
such that
, is a dense subset of
, and the set of functions with this property is residual in
. We will show that in
and some related Banach spaceX there are functionsf with
is dense in
, and we will give a sufficient condition when the set of such functions is residual inX. 相似文献
4.
Marian Nowak 《Czechoslovak Mathematical Journal》2000,50(2):401-414
Let
be a real Banach space and let E be an ideal of L
0 over a -finite measure space (, , ). Let (X) be the space of all strongly -measurable functions f: X such that the scalar function
, defined by
, belongs to E. The paper deals with strong topologies on E(X). In particular, the strong topology
the order continuous dual of E(X)) is examined. We generalize earlier results of [PC] and [FPS] concerning the strong topologies. 相似文献
5.
The problem of estimating of the law
(in the space
of the paths) and the common marginal distribution for a strictly stationary ergodic process X is discussed. We show, in particular, that:(1) The empirical measure
with probability 1 converges weakly in
to
.(2) The empirical measure
corresponding to the path
, converges a.s. when T in total variation to the marginal law if and only if the local time for X exists. (3) The L
p-convergence of the empirical densities f
T to the marginal one is studied.(4) A version of the CLT for empirical densities f
T provided both the mixing properties and the local time of the underlying process are good enough is given. 相似文献
6.
We study a semigroup of linear operators on a Banach space X which satisfies the condition codim X
0<, where
We show that X
0 is closed and establish some properties of the asymptotic behavior of the subspaces complementing X
0 to X. 相似文献
7.
S. S. Podkorytov 《Journal of Mathematical Sciences》2003,113(6):868-878
Let
. Assume that V is a manifold,
is the set of germs of n-dimensional oriented submanifolds of V, and
is the 2-module of all 2-valued functions on E
n
(V). If
is an oriented submanifold, let
be the indicator function of the set of germs of X. It is proved that there exists a quadratic map
such that for any compact oriented submanifold
one has the relation
, where
is the (rational) semicharacteristic of
, i.e., the residue class defined by the formula
Bibliography: 7 titles. 相似文献
8.
吴启光 《应用数学学报(英文版)》1995,11(4):378-388
QUADRATICESTIMATORSOFQUADRATICFUNCTIONSWITHPARAMETERSINNORMALLINEARMODELS¥WUQIGUANG(吴启光)(InstituteofSystemeScience,theChinese... 相似文献
9.
For a cardinal , we say that a subset B of a space X is C
-compact in X if for every continuous function
is a compact subset of
. If B is a C-compact subset of a space X, then (B, X) denotes the degree of C
-compactness of B in X. A space X is called -pseudocompact if X is C
-compact into itself. For each cardinal , we give an example of an -pseudocompact space X such that X × X is not pseudocompact: this answers a question posed by T. Retta in Some cardinal generalizations of pseudocompactness Czechoslovak Math. J. 43 (1993), 385–390. The boundedness of the product of two bounded subsets is studied in some particular cases. A version of the classical Glicksberg's Theorem on the pseudocompactness of the product of two spaces is given in the context of boundedness. This theorem is applied to several particular cases. 相似文献
10.
Let {\bold x}[] be a stationary Gaussian process with zero mean and spectral density f, let
be the -algebra induced by the random variables {\bold x}[], D(R1), and let
t, t > 0, be the -algebra induced by the random variables x[],supp [-t,t]. Denote by
(f) the Gaussian measure on
generated by {\bold x}. Let
t(f) be the restriction of
(f) to
t. Let f and g be nonnegative functions such that the measures
t(f) and
t(g) are absolutely continuous. Put
For a fixed g(u) and for f(u)= ft(u) close to g(u) in some sense, the asymptotic normality of
t(f,g) is proved under some regularity conditions. Bibliography: 14 titles. 相似文献
11.
H. Fiedler 《Numerische Mathematik》1987,51(5):571-581
Summary Interpolatory quadrature formulae consist in replacing
by
wherep
f
denotes the interpolating polynomial off with respect to a certain knot setX. The remainder
may in many cases be written as
wherem=n resp. (n+1) forn even and odd, respectively. We determine the asymptotic behaviour of the Peano kernelP
X
(t) forn for the quadrature formulae of Filippi, Polya and Clenshaw-Curtis. 相似文献
12.
M. Emery 《Probability Theory and Related Fields》1980,51(1):95-100
Summary Let (,
, P) be a complete probability space; let
t0 be an increasing right-continuous family of
-complete sub--fields of
; let
be a sequence of semimartingales. Assume that for all positive t and for all bounded predictable processes H, the r.v.'s
converge in probability to a limit J(t, H) when n tends to infinity. Then there exists a semimartingale X such that, for all t and H, J(t, H)=
. 相似文献
13.
Shiquan WU 《应用数学学报(英文版)》1996,12(4):377-383
Letn, s
1,s
2, ... ands
n
be positive integers. Assume
is an integer for eachi}. For
,
, and
, denotes
p
(a)={j|1jn,a
j
p},
, and
.
is called anI
t
p
-intersecting family if, for any a,b
,a
i
b
i
=min(a
i
,b
i
)p for at leastt i's.
is called a greedyI
t
P
-intersecting family if
is anI
t
p
-intersecting family andW
p
(A)W
p
(B+A
c
) for anyAS
p
(
) and any
with |B|=t–1.In this paper, we obtain a sharp upper bound of |
| for greedyI
t
p
-intersecting families in
for the case 2ps
i
(1in) ands
1>s
2>...>s
n
.This project is partially supported by the National Natural Science Foundation of China (No.19401008) and by Postdoctoral Science Foundation of China. 相似文献
14.
А. О. кАРАпЕтьН 《Analysis Mathematica》1994,20(3):185-203
Let B n be a domain and (y), y B and arbitrary positive, continuous function. If p, s (0, +), denote byH
s,
p
(T
B
) the class of the functionsf(z)f(x+iy), holomorphic in the tube domain
相似文献
15.
In the present paper we obtain a sufficient condition for the exponential dichotomy of a strongly continuous, one-parameter
semigroup , in terms of the admissibility of the pair . It is already known the equivalence between the -admissibility condition and and the hyperbolicity of a C
0-semigroup , when we assume a priori that the kernel of the dichotomic projector (denoted here by X
2) is T(t)-invariant and is an invertible operator. We succeed to prove in this paper that the admissibility of the pair still implies the existence of an exponential dichotomy for a C
0-semigroup even in the general case where the kernel of the dichotomic projector, X
2, is not assumed to be T(t)-invariant.
相似文献
16.
The asymptotic behaviour of bounded solutions of evolutionary integral equations in a Banach spaceX
17.
Let X be an open subset of
n and (f1, ...,fp): X
p be a holomorphic mapping. We prove that if (x0,0, 0) T* ×
p does not belong to the characteristic variety of the
X []-module
X[]f, then there exists a conic neighborhood V × of (x0, 0) such the function
is rapidely decreasing in | Im | for with Re bounded, for any (n,n)-form of class C with compact support in V. The following partial converse of this result is also established: if
for all (n,n)-forms of class C with compact support in X, then
. 相似文献
18.
Let X be a rearrangement-invariant Banach function space
over a complete probability space
, and denote by
the Hardy space consisting of all martingales
such that
. We prove that
implies
for any filtration
if and only if Doobs inequality holds in
X, where
denotes the martingale defined by
, n = 0, 1, 2, ..., and
a.s.Received: 1 August 2000 相似文献
19.
The automorphism group of the Barnes-Wall lattice L
m in dimension 2
m
(m ; 3) is a subgroup of index 2 in a certain Clifford group
of structure 2
+
1+2m
. O
+(2m,2). This group and its complex analogue
of structure
.Sp(2m, 2) have arisen in recent years in connection with the construction of orthogonal spreads, Kerdock sets, packings in Grassmannian spaces, quantum codes, Siegel modular forms and spherical designs. In this paper we give a simpler proof of Runge@apos;s 1996 result that the space of invariants for
of degree 2k is spanned by the complete weight enumerators of the codes
, where C ranges over all binary self-dual codes of length 2k; these are a basis if m k - 1. We also give new constructions for L
m and
: let M be the
-lattice with Gram matrix
. Then L
m is the rational part of M
m, and
= Aut(Mm). Also, if C is a binary self-dual code not generated by vectors of weight 2, then
is precisely the automorphism group of the complete weight enumerator of
. There are analogues of all these results for the complex group
, with doubly-even self-dual code instead of self-dual code. 相似文献
20.
T. I. Seidman 《Journal of Optimization Theory and Applications》1980,30(4):535-547
One standard approach to solvingf(x)=b is the minimization of f(x)–b2 overx in
, where
corresponds to a parametric representation providing sufficiently good approximation to the true solutionx*. Call the minimizerx=A(
). Take
=
N
for a sequence {
N
} of subspaces becoming dense, and so determine an approximating sequences {x
N
A (
N
)}. It is shown, withf linear and one-to-one, that one need not havex
Nx* iff
–1 is not continuous.This work was supported by the US Army Research Office under Grant No. DAAG-29-77-G-0061. The author is indebted to the late W. C. Chewning for suggesting the topic in connection with computing optimal boundary controls for the heat equation (Ref. 2). 相似文献
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