共查询到20条相似文献,搜索用时 292 毫秒
1.
Summary We examine local geometric properties of level sets of the Brownian sheet, and in particular, we identify the asymptotic distribution of the area of sets which correspond to excursions of the sheet high above a given level in the neighborhood of a particular random point. It is equal to the area of certain individual connected components of the random set {(s, t):B(t)>b(s)}, whereB is a standard Brownian motion andb is (essentially) a Bessel process of dimension 3. This limit distribution is studied and, in particular, explicit formulas are given for the probability that a point belongs to a specific connected component, and for the expected area of a component given the height of the excursion ofB(t)-b(s) in this component. These formulas are evaluated numerically and compared with the results from direct simulations ofB andb.The research of this author was partially supported by grants DMS-9103962 from the National Science Foundation and DAAL03-92-6-0323 from the Army Research Office 相似文献
2.
We study the L-series of cubic fourfolds. Our main result is that, if X/C is a special cubic fourfold associated to some polarized K3 surface S, defined over a number field K and satisfying , then X has a model over K such that the L-series of the primitive cohomology of X/K can be expressed in terms of the L-series of S/K. This allows us to compute the L-series for a discrete dense subset of cubic fourfolds in the moduli spaces of certain special cubic fourfolds. We also discuss
a concrete example. 相似文献
3.
Srinivasa R. Arikati C. Pandu Rangan Glenn K. Manacher 《BIT Numerical Mathematics》1991,31(2):181-193
An efficient reduction process for path problems on circular-arc graphs is introduced. For the parity path problem, this reduction gives anO(n+m) algorithm for proper circular-arc graphs, and anO(n+m) algorithm for general circular-arc graphs. This reduction also gives anO(n+m) algorithm for the two path problem on circular-arc graphs. 相似文献
4.
Summary We describe geometric properties of {W>}, whereW is a standard real-valued Brownian sheet, in the neighborhood of the first hitP of the level set {W>} along a straight line or smooth monotone curveL. In such a neighborhood we use a decomposition of the formW(s, t)=–b(s)+B(t)+x(s, t), whereb(s) andB(t) are particular diffusion processes andx(s, t) is comparatively small, to show thatP is not on the boundary of any connected component of {W>}. Rather, components of this set form clusters nearP. An integral test for thorn-shaped neighborhoods ofL with tip atP that do not meet {W>} is given. We then analyse the position and size of clusters and individual connected components of {W>} near such a thorn, giving upper bounds on their height, width and the space between clusters. This provides a local picture of the level set. Our calculations are based on estimates of the length of excursions ofB andb and an accounting of the error termx.The research of this author was partially supported by NSF grant DMS-9103962, and, during the period of revision, by grant DAAL03-92-6-0323 from the Army Research Office 相似文献
5.
Gregor Kemper 《manuscripta mathematica》1996,90(1):343-363
A general method is developed to attack Noether's Problem constructively by trying to find minimal bases consisting of rational
invariants which are quotients of polynomials of small degrees. This approach turns out to be successful for many small groups
and for most of the classical groups with their natural representations. The applications include affirmative answers to Noether's
Problem for the conformal symplectic groups CSp
2n
(q), for the simple subgroups Ω
n
(q) of the orthogonal groups forn andq odd, for some other subgroups of orthogonal groups and for the special unitary groups SU
n
(q
2).
The author was supported by the Graduate College “Modelling and Scientific Computing in Mathematics and Science” during this
work 相似文献
6.
A setE ofk edges in a multigraphG=(V,E) is said to be ak most vital edge set (k-MVE set) if these edges being removed fromG, the resultant graphG=(V,E –E) has minimum number of spanning trees. The problem of finding ak-MVE set for two-terminal series-parallel graphs is considered in this paper. We present anO (|E|) time algorithm for the casek=1, and anO(|V|
k
+|E|) time algorithm for arbitraryk. 相似文献
7.
Jussi Klemelä 《Probability Theory and Related Fields》2006,134(4):539-564
Estimation of a quadratic functional of a function observed in the Gaussian white noise model is considered. A data-dependent
method for choosing the amount of smoothing is given. The method is based on comparing certain quadratic estimators with each
other. It is shown that the method is asymptotically sharp or nearly sharp adaptive simultaneously for the “regular” and “irregular”
region. We consider lp bodies and construct bounds for the risk of the estimator which show that for p=4 the estimator is exactly optimal and for example when p ∈[3,100], then the upper bound is at most 1.055 times larger than the lower bound. We show the connection of the estimator
to the theory of optimal recovery. The estimator is a calibration of an estimator which is nearly minimax optimal among quadratic
estimators.
Writing of this article was financed by Deutsche Forschungsgemeinschaft under project MA1026/6-2, CIES, France, and Jenny
and AnttiWihuri Foundation. 相似文献
8.
We prove two ``large images' results for the Galois representations attached to a degree d Q-curve E over a quadratic field K: if K is arbitrary, we prove maximality of the image for every prime p>13 not dividing d, provided that d is divisible by q (but d≠q) with q=2 or 3 or 5 or 7 or 13. If K is real we prove maximality of the image for every odd prime p not dividing d
D, where D= disc(K), provided that E is a semistable Q-curve. In both cases we make the (standard) assumptions that E does not have potentially good reduction at all primes p∤6 and that d is square free.
The first author is supported by BFM2003-06092. 相似文献
9.
Ola Hössjer 《Probability Theory and Related Fields》1996,105(2):159-192
Summary We consider a general class of varying bandwidth estimators of a probability density function. The class includes the Abramson estimator, transformation kernel density estimator (TKDE), Jones transformation kernel density estimator (JTKDE), nearest neighbour type estimator (NN), Jones-Linton-Nielsen estimator (JLN), Taylor series approximations of TKDE (TTKDE) and Simpson's formula approximations of TKDE (STKDE). Each of these estimators needs a pilot estimator. Starting with an ordinary kernel estimator
, it is possible to iterate and compute a sequence of estimates
, using each estimate as a pilot estimator in the next step. The first main result is a formula for the bias order. If the bandwidths used in different steps have a common orderh=h(n), the bias of
is of orderh
2km
,k=1, ...,t. Hereh
m
is the bias order of the ideal estimator (defined by using the unknownf as pilot). The second main result is a recursive formula for the leading bias and stochastic terms in an asymptotic expansion of the density estimates. Ifm<, it is possible to make
asymptotically equivalent to the ideal estimator. 相似文献
10.
We study the uniqueness of norm-preserving extension of n-homogeneous polynomials on X, where X is a c0-sum of Hilbert spaces. We show that there exists a unique norm-preserving extension for norm-attaining 2-homogeneous polynomials on X to X″, but this result fails for homogeneous polynomials of degree greater than 2. 相似文献
11.
In this paper we study the limit distributions of extreme, intermediate and central m-generalized order statistics, as well as m-dual generalized order statistics, of a stationary Gaussian sequence under equi-correlated set up. Moreover, the result of extremes is extended to a wide subclass of generalized order statistics, as well as dual generalized order statistics, when the parameters γ1,n, γ2,n,?…?, γn,n are assumed to be pairwise different. 相似文献
12.
13.
Martin N. Ndumu 《Potential Analysis》1996,5(4):311-356
Let M be a complete connected Riemannian manifold and let N be a submanifold of M. Let v: E
v»N be the normal bundle of N and exp
v
: E
v»M its exponential map.Let (exp
infv
/sup-1
, M
0) be the Fermi chart relative to the submanifold N. Then, by using the Fermi coordinates we obtain an integral formula for the Dirichlet heat kernel p
t
m
(-,-). That is, we obtain a probabilistic representation for the integral N
f(y)p
t
M
(x,y) dywhere f is any measurable function of compact support in M
0. This representation involves a submanifold semi-classical Brownian Riemannian bridge process. Then applying the integral formula via a Riemannian submersion in [5], we obtain heat kernel formulae for the complex projective space cP
n, the quaternionic projective space QP
n and the Caley line CaP
1. The case of the Caley plane CaP
2 eludes us due to the lack of a submersion theorem.This work is part of a Ph.D. Thesis which was undertaken under Professor K. D. Elworthy, Mathematics Institute, Warwick University, Coventry CV47AL, England, Great Britain. 相似文献
14.
Given a family {L
0(b,L
1(b)}
b∈B
of pairs of transverse Lagrangian subspaces of a hermitean symplectic vector space we define a family of Dirac operators
on the unit interval and consider itsη-formη(L
0,L
1) εΘ*(B). To a family {L
0(b,L
1(b,L
2(b)}
b∈B
of pairwise transverse Lagrangian subspaces we associate the cocycleη(L
0,L
1)+η(L
1,L
2)+η(L
2,L
1) which is a closed form. We identify its cohomology class with a generalization to families of the triple Maslov index. 相似文献
15.
Günter Last 《Probability Theory and Related Fields》1994,99(3):361-388
Summary We consider a point process with the Polish phase space (X,X) and a system of -fields (x),xX, generated by on certain sets (x)X. We define predictability for random processes indexed byX and for random measures onX and prove the existence and uniqueness of predictable and dual predictable projections under a regularity condition on . ForX=
2
+
and under monotonicity assumptions on the sets x we will identify the predictable projections of some simple processes as regular versions of certain martingales. 相似文献
16.
Suppose k is a field. Let A and B be two finite dimensional k-algebras such that there is a stable equivalence of Morita type between A and B. In this paper, we prove that (1) if A and B are representation-finite then their Auslander algebras are stably equivalent of Morita type; (2) The n-th Hochschild homology groups of A and B are isomorphic for all n≥1. A new proof is also provided for Hochschild cohomology groups of self-injective algebras under a stable equivalence of Morita type. 相似文献
17.
U. Stadtmüller 《Periodica Mathematica Hungarica》1986,17(2):83-108
We consider a class of nonparametric estimators for the regression functionm(t) in the model:y
i
=m(t
i
) +
i
, 1 i n, t
i
[0, 1], which are linear in the observationsy
i
. Several limit theorems concerning local and global stochastic and a.s. convergence and limit distributions are given. 相似文献
18.
We consider finite-range, nonzero mean, one-dimensional exclusion processes on ℤ. We show that, if the initial configuration
has ``density' α, then the process converges in distribution to the product Bernoulli measure with mean density α. From this we deduce the strong form of local equilibrium in the hydrodynamic limit for non-product initial measures. 相似文献
19.
M. Koppinen 《BIT Numerical Mathematics》1986,26(3):333-338
The purpose of this paper is to describe an algorithm for computing weight multiplicities in a simple module of an algebraic Chevalley group over a field of positive characteristicp. The method is essentially more efficient than the one introduced by N. Burgoyne in 1971, especially whenp is small. A concrete application is outlined whereG is of typeG
2 andp=5. 相似文献
20.
In this work, we determine all modular curves X1(M,N) which are bielliptic, and then we also discuss the problem of finding the curves X1(M,N) which admit infinitely many quartic points over . 相似文献