共查询到20条相似文献,搜索用时 31 毫秒
1.
David Slepian 《Stochastic Processes and their Applications》1983,14(3):249-265
Let X(t) be the ergodic Gauss–Markov process with mean zero and covariance function e?|τ|. Let D(t) be +1, 0 or ?1 according as X(t) is positive, zero or negative. We determine the non-linear estimator of X(t1) based solely on D(t), ?T ? t ? 0, that has minimal mean–squared error ε2(t1, T). We present formulae for ε2(t1, T) and compare it numerically for a range of values of t1 and T with the best linear estimator of X(t1) based on the same data. 相似文献
2.
James B. Shearer 《Discrete Mathematics》1983,46(1):83-87
Let G be a triangle-free graph on n points with average degree d. Let α be the independence number of G. In this note we give a simple proof that α ? n (d ln d ? d + 1)/(d ? 1)2. We also consider what happens when G contains a limited number of triangles. 相似文献
3.
Arno van den Essen Andrzej Nowicki Andrzej Tyc 《Journal of Pure and Applied Algebra》2003,177(1):43-47
Let k be an algebraically closed field of characteristic zero and ℘ a prime ideal in k[X]?k[X1,…,Xn]. Let g∈k[X] and d?1. If for all 1?|α|?d the derivatives ∂αg belong to ℘, then there exists c∈k such that g−c∈℘(d+1), the d+1th symbolic power of ℘. In particular, if ℘ is a complete intersection it follows that g−c∈℘d+1. 相似文献
4.
Renjin Jiang 《Journal of Functional Analysis》2011,261(12):3549-3584
Let (X,d) be a complete, pathwise connected metric measure space with a locally Ahlfors Q-regular measure μ, where Q>1. Suppose that (X,d,μ) supports a (local) (1,2)-Poincaré inequality and a suitable curvature lower bound. For the Poisson equation Δu=f on (X,d,μ), Moser-Trudinger and Sobolev inequalities are established for the gradient of u. The local Hölder continuity with optimal exponent of solutions is obtained. 相似文献
5.
Wolfhard Hansen 《Journal of Functional Analysis》2005,226(2):452-484
Let D be a bounded open subset in Rd, d?2, and let G denote the Green function for D with respect to (-Δ)α/2, 0<α?2, α<d. If α<2, assume that D satisfies the interior corkscrew condition; if α=2, i.e., if G is the classical Green function on D, assume—more restrictively—that D is a uniform domain. Let g=G(·,y0)∧1 for some y0∈D. Based on the uniform boundary Harnack principle, it is shown that G has the generalized triangle property which states that when d(z,x)?d(z,y). An intermediate step is the approximation G(x,y)≈|x-y|α-dg(x)g(y)/g(A)2, where A is an arbitrary point in a certain set B(x,y).This is discussed in a general setting where D is a dense open subset of a compact metric space satisfying the interior corkscrew condition and G is a quasi-symmetric positive numerical function on D×D which has locally polynomial decay and satisfies Harnack's inequality. Under these assumptions, the uniform boundary Harnack principle, the approximation for G, and the generalized triangle property turn out to be equivalent. 相似文献
6.
Let Xt be a homogeneous Markov process generated by the weak infinitesimal operator A. Let be the class of functions f such that f, f2?DA, the domain of A. The main result of this paper states that for ? ∈ can be represented by a stochastic integral and other terms. If the process is generated by a second order differential operator (with ‘poor’ coefficients possibly) on C02(Rd) then the process itself can be represented as the solution of an Itô stochastic differential equation. 相似文献
7.
Eugene B. Dynkin 《Comptes Rendus Mathematique》2004,338(8):605-610
Let X=(XD,Pμ) be a superdiffusion in a domain . We introduce a germ σ-algebra at the boundary of E and we prove that, on this σ-algebra, Pμ1 is absolutely continuous with respect to Pμ2 if μ1 and μ2 are concentrated on compact subsets of E. In combination with previous results of Dynkin, Kuznetsov and Mselati, this leads to a complete classification of positive solutions of equation Δu=uα in a bounded domain E of class C4 for the case 1<α?2. To cite this article: E.B. Dynkin, C. R. Acad. Sci. Paris, Ser. I 338 (2004). 相似文献
8.
Štefko Miklavi? 《Linear algebra and its applications》2009,430(1):251-636
Let Γ denote a distance-regular graph with diameter D?3. Assume Γ has classical parameters (D,b,α,β) with b<-1. Let X denote the vertex set of Γ and let A∈MatX(C) denote the adjacency matrix of Γ. Fix x∈X and let A∗∈MatX(C) denote the corresponding dual adjacency matrix. Let T denote the subalgebra of MatX(C) generated by A,A∗. We call T the Terwilliger algebra of Γ with respect to x. We show that up to isomorphism there exist exactly two irreducible T-modules with endpoint 1; their dimensions are D and 2D-2. For these T-modules we display a basis consisting of eigenvectors for A∗, and for each basis we give the action of A. 相似文献
9.
Let X={Xt,t?0} be a symmetric Markov process in a state space E and D an open set of E. Denote by XD the subprocess of X killed upon leaving D. Let S={St,t?0} be a subordinator with Laplace exponent φ that is independent of X. The processes Xφ?{XSt,t?0} and are called the subordinate processes of X and XD, respectively. Under some mild conditions, we show that, if {-μn,n?1} and {-λn,n?1} denote the eigenvalues of the generators of the subprocess of Xφ killed upon leaving D and of the process XD respectively, then
10.
Let R be a K-algebra acting densely on VD, where K is a commutative ring with unity and V is a right vector space over a division K-algebra D. Let ρ be a nonzero right ideal of R and let f(X1,…,Xt) be a nonzero polynomial over K with constant term 0 such that μR≠0 for some coefficient μ of f(X1,…,Xt). Suppose that d:R→R is a nonzero derivation. It is proved that if rankd(f(x1,…,xt))?m for all x1,…,xt∈ρ and for some positive integer m, then either ρ is generated by an idempotent of finite rank or d=ad(b) for some b∈End(VD) of finite rank. In addition, if f(X1,…,Xt) is multilinear, then b can be chosen such that rank(b)?2(6t+13)m+2. 相似文献
11.
Helma GladdinesMarcel van de Vel 《Topology and its Applications》2011,158(3):424-431
The disconnection number d(X) is the least number of points in a connected topological graph X such that removal of d(X) points will disconnect X (Nadler, 1993 [6]). Let Dn denote the set of all homeomorphism classes of topological graphs with disconnection number n. The main result characterizes the members of Dn+1 in terms of four possible operations on members of Dn. In addition, if X and Y are topological graphs and X is a subspace of Y with no endpoints, then d(X)?d(Y) and Y obtains from X with exactly d(Y)−d(X) operations. Some upper and lower bounds on the size of Dn are discussed.The algorithm of the main result has been implemented to construct the classes Dn for n?8, to estimate the size of D9, and to obtain information on certain subclasses such as non-planar graphs (n?9) and regular graphs (n?10). 相似文献
12.
Jinghai Shao 《Bulletin des Sciences Mathématiques》2006,130(8):720-738
Let (X,ρ) be a Polish space endowed with a probability measure μ. Assume that we can do Malliavin Calculus on (X,μ). Let be a pseudo-distance. Consider QtF(x)=infy∈X{F(y)+d2(x,y)/2t}. We shall prove that QtF satisfies the Hamilton-Jacobi inequality under suitable conditions. This result will be applied to establish transportation cost inequalities on path groups and loop groups in the spirit of Bobkov, Gentil and Ledoux. 相似文献
13.
Let Xt be a Cauchy process in . We investigate some of the fine spectral theoretic properties of the semigroup of this process killed upon leaving a domain D. We establish a connection between the semigroup of this process and a mixed boundary value problem for the Laplacian in one dimension higher, known as the “Mixed Steklov Problem.” Using this we derive a variational characterization for the eigenvalues of the Cauchy process in D. This characterization leads to many detailed properties of the eigenvalues and eigenfunctions for the Cauchy process inspired by those for Brownian motion. Our results are new even in the simplest geometric setting of the interval (−1,1) where we obtain more precise information on the size of the second and third eigenvalues and on the geometry of their corresponding eigenfunctions. Such results, although trivial for the Laplacian, take considerable work to prove for the Cauchy processes and remain open for general symmetric α-stable processes. Along the way we present other general properties of the eigenfunctions, such as real analyticity, which even though well known in the case of the Laplacian, are not available for more general symmetric α-stable processes. 相似文献
14.
Let 𝒲 be the Virasoro-like algebra, and d 1, d 2 be the degree derivations of 𝒲. Set ? = W⊕C d 1⊕C d 2. Let F α(V) be the ?-module defined by Larsson's functor applied to a finite dimensional sl 2-module V. In this article, the derivations from ? to ?-modules F α(V) and the first cohomology group H 1(?, F α(V)) are given. 相似文献
15.
Youri Davydov 《Statistics & probability letters》2012,82(1):145-150
We consider the problem of the convergence of the so-called LePage series in the Skorokhod space Dd=D([0,1],Rd) and provide a simple criterion based on the moments of the increments of the random process involved in the series. This provides a simple sufficient condition for the existence of an α-stable distribution on Dd with given spectral measure. 相似文献
16.
Dončo Dimovski 《Topology and its Applications》1985,21(2):147-157
Let (W4,?W4) be a 4-manifold. Let f1,f2,…,fk:(D2,?D2)→ (W4,?W4) be transverse immersions that have spherical duals . Then there are open disjoint subsets V1, V2,…,Vk of W, such that for each 1?i?k, (a) ?Vi=V1∩?W and ?Vi is an open regular neighborhood of fi(?D2) in ?W, and (b) (Vi,?Vi,fi(?D2)) is proper homotopy equivalent to (M, ?M, d)—a standard object in which d bounds an embedded flat disk. If we could get a homeomorphism instead of a proper homotopy equivalence, then we would be able to prove a 5-dimensional s-cobordism theorem. 相似文献
17.
Let (X,d X ) and (Y,d Y ) be semimetric spaces with distance sets D(X) and D(Y), respectively. A mapping F:?X→Y is a weak similarity if it is surjective and there exists a strictly increasing f:?D(Y)→D(X) such that d X =f°d Y °(F?F). It is shown that the weak similarities between geodesic spaces are usual similarities and every weak similarity F:?X→Y is an isometry if X and Y are ultrametric and compact with D(X)=D(Y). Some conditions under which the weak similarities are homeomorphisms or uniform equivalences are also found. 相似文献
18.
R.J. Williams 《Advances in Applied Mathematics》1985,6(1):1-3
Let {Xt, t ≥ 0} be Brownian motion in d (d ≥ 1). Let D be a bounded domain in d with C2 boundary, ?D, and let q be a continuous (if d = 1), Hölder continuous (if d ≥ 2) function in D?. If the Feynman-Kac “gauge” Ex{exp(∝0τDq(Xt)dt)1A(XτD)}, where τD is the first exit time from D, is finite for some non-empty open set A on ?D and some x?D, then for any ), is the unique solution in of the Schrödinger boundary value problem . 相似文献
19.
Michel Las Vergnas 《Discrete Mathematics》1976,15(1):27-39
The main result of this paper is the following theorem: Let G = (X,E) be a digraph without loops or multiple edges, |X| ?3, and h be an integer ?1, if G contains a spanning arborescence and if d+G(x)+d?G(x)+d?G(y)+d?G(y)? 2|X |?2h?1 for all x, y?X, x ≠ y, non adjacent in G, then G contains a spanning arborescence with ?h terminal vertices. A strengthening of Gallai-Milgram's theorem is also proved. 相似文献
20.
Euisung Park 《Journal of Pure and Applied Algebra》2010,214(2):101-111
Let X be a hyperelliptic curve of arithmetic genus g and let f:X→P1 be the hyperelliptic involution map of X. In this paper we study higher syzygies of linearly normal embeddings of X of degree d≤2g. Note that the minimal free resolution of X of degree ≥2g+1 is already completely known. Let A=f∗OP1(1), and let L be a very ample line bundle on X of degree d≤2g. For , we call the pair (m,d−2m)the factorization type ofL. Our main result is that the Hartshorne-Rao module and the graded Betti numbers of the linearly normal curve embedded by |L| are precisely determined by the factorization type of L. 相似文献