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1.
The local time of iterated Brownian motion 总被引:1,自引:0,他引:1
We define and study the local time process {L
*(x,t);x1,t0} of the iterated Brownian motion (IBM) {H(t):=W
1(|W
2
(t)|); t0}, whereW
1(·) andW
2(·) are independent Wiener processes.Research supported by Hungarian National Foundation for Scientific Research, Grant No. T 016384.Research supported by an NSERC Canada Grant at Carleton University, Ottawa.Research supported by a PSC CUNY Grant, No. 6-66364. 相似文献
2.
We discuss the relations among the best approximation E
n
(f) and the Fourier coefficients of a function, under the conditions that and , where MVBVS* is the class of the so-called Strong Mean Value Bounded Variation Sequences.
This work was supported by NSERC RCD grant and AARMS of Canada (Yu D S), by NSERC of Canada (Zhou P), and by the National
Natural Science Foundation of China (Grant No. 10471130) and the Open Fund (Grant No. PLN0613) of State Key Laboratory of
Oil and Gas Reservoir Geology and Exploitation (Southwest Petroleum University) (Zhou S P) 相似文献
3.
B. Yousefi 《Rendiconti del Circolo Matematico di Palermo》2002,51(3):403-410
Let
be a sequence of positive numbers and 1≤p<∞. We consider the spaceH
p(β) of all power series
such that Σ|
(n)|p β(n
p<∞. We investigate regions on which our formal power series represent bounded analytic functions.
Research partially supported by the Shiraz University Research Council Grant No. 79-SC-1311-675. 相似文献
4.
Generalizing earlier results, it is shown that if are “large” subsets of a finite field F
q
, then the equations a + b = cd, resp. ab + 1 = cd can be solved with . Other algebraic equations with solutions restricted to “large” subsets of F
q
are also studied. The proofs are based on character sum estimates proved in Part I of the paper.
Research partially supported by the Hungarian National Foundation for Scientific Research, Grants No. T 043623, T 043631 and
T 049693. 相似文献
5.
Let {X
k
,k=1,2,…} be a sequence of independent binomial variables, with
the Fourier transform of the distribution ofY. Finally denote lim [P
k
− 1/2] byδ. We haveTheorem.
Research supported by N.S.F. Grant GP-25736.
Research supported by N.S.F. Grant GP-12365. 相似文献
6.
In this paper the study of which varieties, in a countable similarity type, have non-free
(or equivalently 1-free) algebras is completed. It was previously known that if a variety satisfies a property known as the construction principle then there are such algebras. If a variety does not satisfy the construction principle then either every
-free algebra is free or for every infinite cardinalk, there is a k+-free algebra of cardinality k+ which is not free. Under the set theoretic assumption V=L, for any varietyV in a countable similarity type, either the class of free algebras is definable in
or it is not definable in any
.In Memory of Evelyn NelsonPresented by Ralph McKenzie.Research partially supported by NSERC of Canada Grant #A8948.Research partially supported by NSERC of Canada. The research for this paper was begun while the second author was visiting Simon Fraser University. 相似文献
7.
We prove the following theorem. Assume f ∈ L
∞(R
2) with bounded support. If f is continuous at some point (x
1,x
2) ∈ R
2, then the double Fourier integral of f is strongly q-Cesàro summable at (x
1,x
2) to the function value f(x
1,x
2) for every 0 < q < ∞. Furthermore, if f is continuous on some open subset
of R
2, then the strong q-Cesàro summability of the double Fourier integral of f is locally uniform on
.
Research partially supported by the Australian Research Council and the Hungarian National Foundation for Scientific Research
under Grant T 046 192. 相似文献
8.
In this paper we obtain non-isotropic weighted L
p
estimates with the boundary distance weight function for the -equation on piecewise smooth strictly pseudoconvex domains under a hypothesis of complex transversality in ℂn using the explicit formula of solutions by Berndtsson-Andersson.
This work was supported by the Korea Research Foundation Grant funded by Korea Government (MOEHRD, Basic Research Promotion
Fund) (Grant No. KRF-2005-070-C00007) 相似文献
9.
In this paper, we study the complexity of information of approximation problem on the multivariate Sobolev space with bounded mixed derivative MWpr,α(Td), 1 < p < ∞, in the norm of Lq(Td), 1 < q < ∞, by adaptive Monte Carlo methods. Applying the discretization technique and some properties of pseudo-s-scale, we determine the exact asymptotic orders of this problem. 相似文献
10.
In this paper,we explore some weakly consistent properties of quasi-maximum likelihood estimates(QMLE) concerning the quasi-likelihood equation in=1 Xi(yi-μ(Xiβ)) = 0 for univariate generalized linear model E(y |X) = μ(X'β).Given uncorrelated residuals {ei = Yi-μ(Xiβ0),1 i n} and other conditions,we prove that βn-β0 = Op(λn-1/2) holds,where βn is a root of the above equation,β0 is the true value of parameter β and λn denotes the smallest eigenvalue of the matrix Sn = ni=1 XiXi.We also show that the convergence rate above is sharp,provided independent non-asymptotically degenerate residual sequence and other conditions.Moreover,paralleling to the elegant result of Drygas(1976) for classical linear regression models,we point out that the necessary condition guaranteeing the weak consistency of QMLE is Sn-1→ 0,as the sample size n →∞. 相似文献
11.
M. Taghavi 《Rendiconti del Circolo Matematico di Palermo》1999,48(2):237-242
The quotient of
divided by
, whereP is a self-inversive and unimodular polynomial of any degree, dominates an absolute constantK>1. A 1989 paper gaveK=1.0252 on which its authors conjetured that the best constant is
. We supply counter examples to their claim and provide a partial result for whenever theL
q norm is replaced by some “discrete” type norm.
Research supported by the Shiraz University Grant 72-SC-784-432. 相似文献
12.
Let X be a complex Banach space with norm ‖ · ‖, B be the unit ball in X, D
n
be the unit polydisc in ℂ
n
. In this paper, we introduce a class of holomorphic mappings on B or D
n
. Let f(x) be a normalized locally biholomorphic mapping on B such that (Df(x))−1
f(x) ∈ and f(x) − x has a zero of order k + 1 at x = 0. We obtain coefficient estimates for f(x). These results unify and generalize many known results.
This work was supported by National Natural Science Foundation of China (Grant No. 10571164), Specialized Research Fund for
the Doctoral Program of Higher Education (Grant No. 20050358052), the Jiangxi Provincial Natural Science Foundation of China
(Grant No. 2007GZS0177) and Specialized Research Fund for the Doctoral Program of Jiangxi Normal University. 相似文献
13.
It is proposed that the Gaussian type distribution constantb
qi in the Gaussian model depends on the coordination numberq
i of sitei, and that the relation
holds amongb
qi
’s. The Gaussian model is then studied on a family of the diamond-type hierarchical (or DH) lattices, by the decimation real-space
renormalization group following spin-rescaling method. It is found that the magnetic property of the Gaussian model belongs
to the same universal class, and that the critical pointK* and the critical exponentv are given by
and
, respectively.
Project supported by the National Natural Science Foundation of China (Grant No. 19775008), the National Basic Research
Project supported by the National Natural Science Foundation of China (Grant No. 19775008), the National Basic Research
Project supported by the National Natural Science Foundation of China (Grant No. 19775008), the National Basic Research 相似文献
14.
WenMing Wu 《中国科学A辑(英文版)》2008,51(11):2081-2088
Given the hyperbolic measure dxdy/y
2 on the upper half plane ℍ, the rational actions of PSL2(ℝ) on ℍ induces a continuous unitary representation α of this group on the Hilbert space L
2(ℍ, dxdy/y
2). Supposing that = {M
f
: f ∈ L
∞ (ℍ, dxdy/y
2)}, we show that the crossed product is of type I. In fact, the crossed product is *-isomorphic to the von Neumann algebra , where is the abelian group von Neumann algebra generated by the left regular representation of K.
This work was supported by the Youth Foundation of Sichuan Education Department of China (Grant No. 2003B017) 相似文献
15.
Eberhard MALKOWSKY M. MURSALEEN Suthep SUANTAI 《数学学报(英文版)》2007,23(3):521-532
Let p = (pk)k=0^∞ be a bounded sequence of positive reals, m C N and u be s sequence of nonzero terms. If x = (xk)k=0^∞ is any sequence of complex numbers we write Δ(m)x for the sequence of the m th order differences of x and Δu^(m)X = {x=(x)k=0^∞ uΔ(m)x ∈ X} for any set X of sequences. We determine the α-, β- and γ-duals of the sets Δμ^(m)X for X=co(p),c(p),l∞(p) and characterize some matrix transformations between these spaces Δ^(m)X. 相似文献
16.
LetX
1,X
2,...be a sequence of i.i.d. random variables and putS
0=0,S
n
=X
1+...+X
n
. A strong approximation type result is given forA
N
=
i=1
N
f(S
i
) whereF(x),xR is a real valued function. A similar result is given for
0
t
g(B(s))ds. Some weak convergence type implications are also discussed.1991 Mathematics Subject Classification: Primary: 60F15, Secondary: 60J15.Supported by the Hungarian National Foundation for Scientific Research, Grant No. 1905.Supported by an NSERC Canada Grant at Carleton University.Supported by a PSC CUNY Grant No.662349. 相似文献
17.
We present several partial results, variants, and
consistency results concerning the following (as yet unsolved)
conjecture. If X is a graph
on the ground set V with
then
X has an edge coloring
F with
colors such that if
V is decomposed into
parts then there is one
in which F assumes all
values.Due to some unfortunate misunderstandings, this
paper appeared much later than we expected.* Research partially supported by NSF grants
DMS-9704477 and DMS-0072560. Research partially supported by Hungarian National
Research Grant T 032455. 相似文献
18.
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
19.
We consider the weighted Hardy integral operatorT:L
2(a, b) →L
2(a, b), −∞≤a<b≤∞, defined by
. In [EEH1] and [EEH2], under certain conditions onu andv, upper and lower estimates and asymptotic results were obtained for the approximation numbersa
n(T) ofT. In this paper, we show that under suitable conditions onu andv,
where ∥w∥p=(∫
a
b
|w(t)|p
dt)1/p.
Research supported by NSERC, grant A4021.
Research supported by grant No. 201/98/P017 of the Grant Agency of the Czech Republic. 相似文献
20.
SoYoung Choi 《Israel Journal of Mathematics》2008,165(1):93-101
We find congruences for the t-expansion coefficients of Drinfeld modular forms for
. We give generalized analogies of Siegel’s classical observation on SL
2(ℤ) by determining all the linear relations among the initial t-expansion coefficients of Drinfeld modular forms for
. As a consequence spaces M
k
0
are identified, in which there are congruences for the s-expansion coefficients.
This work was supported by KOSEF R01-2006-000-10320-0 and by the Korea Research Foundation Grant (KRF-2005-214-M01-2005-000-10100-0) 相似文献