共查询到20条相似文献,搜索用时 62 毫秒
1.
Olav Kallenberg 《Stochastic Processes and their Applications》1979,9(2):155-161
Given a random measure η and a fixed number p>1, the Lp-intensity 6η6p of ηis defined as the total variation measure of the subadditive set function 6η(·)6p. It is shown that 6η6p can exist (be locally finite) only if the usual intensity measure Eη exists and a.s, and that in this case . If η is the conditional intensity of a simple point process ξ, then 6η6p equals the total variation of the subadditive set functions 6P[ξB = 1|Bcξ]6p and 6E[ξB|Bcξ]6p. Some applications to stochastic geometry and particle systems are discussed briefly. 相似文献
2.
Jean Bourgain 《Comptes Rendus Mathematique》2002,335(6):529-531
We consider quasi-periodic Schrödinger operators H on of the form H=Hλ,x,ω=λv(x+nω)δn,n′+Δ where v is a non-constant real analytic function on the d-torus and Δ denotes the discrete lattice Laplacian on . Denote by Lω(E) the Lyapounov exponent, considered as function of the energy E and the rotation vector . It is shown that for |λ|>λ0(v), there is the uniform minoration for all E and ω. For all λ and ω, Lω(E) is a continuous function of E. Moreover, Lω(E) is jointly continuous in (ω,E), at any point such that k·ω0≠0 for all . To cite this article: J. Bourgain, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 529–531. 相似文献
3.
A function f(x) defined on = 1 × 2 × … × n where each i is totally ordered satisfying f(x ∨ y) f(x ∧ y) ≥ f(x) f(y), where the lattice operations ∨ and ∧ refer to the usual ordering on , is said to be multivariate totally positive of order 2 (MTP2). A random vector Z = (Z1, Z2,…, Zn) of n-real components is MTP2 if its density is MTP2. Classes of examples include independent random variables, absolute value multinormal whose covariance matrix Σ satisfies ?DΣ?1D with nonnegative off-diagonal elements for some diagonal matrix D, characteristic roots of random Wishart matrices, multivariate logistic, gamma and F distributions, and others. Composition and marginal operations preserve the MTP2 properties. The MTP2 property facilitate the characterization of bounds for confidence sets, the calculation of coverage probabilities, securing estimates of multivariate ranking, in establishing a hierarchy of correlation inequalities, and in studying monotone Markov processes. Extensions on the theory of MTP2 kernels are presented and amplified by a wide variety of applications. 相似文献
4.
H.D Victory 《Journal of Mathematical Analysis and Applications》1982,89(2):420-441
Let K be an eventually compact linear integral operator on , with nonnegative kernel k(x, y), where the underlying measure μ is totally σ-finite on the domain set Ω when p = 1. In considering the equation λf = Kf + g for given nonnegative , P. Nelson, Jr. provided necessary and sufficient conditions, in terms of the support of g, such that a nonnegative solution was attained. Such conditions led to generalizing some of the graph-theoretic ideas associated with the normal form of a nonnegative reducible matrix. The purpose of this paper is to show that the analysis by Nelson can be enlarged to provide a more complete generalization of the normal form of a nonnegative matrix which can be used to characterize the distinguished eigenvalues of K and K1, and to describe sets of support for the eigenfunctions and generalized eigenfunctions of both K and K1 belonging to the spectral radius of K. 相似文献
5.
The set of all rearrangement invariant function spaces on [0,1] having the p-Banach–Saks property has a unique maximal element for all p∈(1,2]. For p=2 this is L2, for p∈(1,2) this is Lp,∞0. We compute the Banach–Saks index for the families of Lorentz spaces , 1?q?∞, and Lorentz–Zygmund spaces L(p,α), , extending the classical results of Banach–Saks and Kadec–Pelczynski for Lp-spaces. Our results show that the set of rearrangement invariant spaces with Banach–Saks index p∈(1,2] is not stable with respect to the real and complex interpoltaion methods. To cite this article: E.M. Semenov, F.A. Sukochev, C. R. Acad. Sci. Paris, Ser. I 337 (2003). 相似文献
6.
Let (m?n) denote the linear space of all m × n complex or real matrices according as = or . Let c=(c1,…,cm)≠0 be such that c1???cm?0. The c-spectral norm of a matrix A?m×n is the quantity . where σ1(A)???σm(A) are the singular values of A. Let d=(d1,…,dm)≠0, where d1???dm?0. We consider the linear isometries between the normed spaces and , and prove that they are dual transformations of the linear operators which map (d) onto (c), where . 相似文献
7.
Following the lines of [13] we introduce the classes of mixed smoothness αp(Rn), αp(Zn) for a multi-index α = (α1,…, αn). Such classes are naturally tied up with the study of semi-elliptic differential and difference equations.Besides a brief presentation of such classes, we concentrate our research on the study of mixed homogeneous multipliers with homogeneity β = (β1, …, βn) and their preservation of mixed homogeneous Hölder classes α∞, for a different multi-index α.In the last paragraph we apply the results to produce various improvements of the classical Schauder's estimates, for differential and difference equations, in the parabolic and elliptic case. 相似文献
8.
Wang Guojun 《Journal of Mathematical Analysis and Applications》1983,94(1):1-23
Let (Ω, , μ) be a probability space and let be a subsigma algebra of . Let A= L∞Ω, , μ , let A= L∞Ω, , μ, and let f?A. It is shown that best L∞-approximations of f by elements of B comprise an interval in B; that is, there exists such that a function g?B is a best L∞-approximation to f if and only if a.e. on Ω. The difference, , of and f is completely characterized in terms of special sets that have been developed in [2]. Then it is established that the best best L∞-approximation, f,∞, to f by elements of B is the average of and , where the function f,∞ is defined by f,∞(ω) limp → ∞f,P(ξ) and f,P denotes the best Lp-approximation to f elements of Lp(Ω, , μ). 相似文献
9.
Let k0 be a finite extension field of the rational numbers, and assume k0 has at least two Zl-extensions. Assume that at least one Zl-extension has Iwasawa invariant μ = 0, and let L be the composite of K and some other Zl-extension of k0. In this paper we find an upper bound for the number of Zl-extensions of k0 contained in L with nonzero μ. 相似文献
10.
M.M. Robertson 《Journal of Number Theory》1977,9(2):258-270
For 1 ≦ l ≦ j, let l = ?h=1q(l){alh + Mv: v = 0, 1, 2,…}, where j, M, q(l) and the alh are positive integers such that j > 1, al1 < … < alq(2) ≦ M, and let l′ = l ∪ {0}. Let p(n : ) be the number of partitions of n = (n1,…,nj) where, for 1 ≦ l ≦ j, the lth component of each part belongs to l and let p1(n : ) be the number of partitions of n into different parts where again the lth component of each part belongs to l. Asymptotic formulas are obtained for p(n : ), p1(n : ) where all but one nl tend to infinity much more rapidly than that nl, and asymptotic formulas are also obtained for p(n : ′), p1(n ; ′), where one nl tends to infinity much more rapidly than every other nl. These formulas contrast with those of a recent paper (Robertson and Spencer, Trans. Amer. Math. Soc., to appear) in which all the nl tend to infinity at approximately the same rate. 相似文献
11.
12.
Václav E. Beneš 《Stochastic Processes and their Applications》1974,2(2):127-140
Girsanov's theorem is a generalization of the Cameron-Martin formula for the derivative of a measure induced by a translation in Wiener space. It states that for ? a nonanticipative Brownian functional with ∫|?|2 ds < ∞ a.s. and with , where , the translated functions are a Wiener process under P?. The Girsanov functionals exp [ζ(?)] have been used in stochastic control theory to define measures corresponding to solutions of stochastic DEs with only measurable control laws entering the right-hand sides. The present aim is to show that these same concepts have direct practical application to final value problems with bounded control. This is done here by an example, the noisy integrator: Make E{x21}∣small, subject to dxt = ut dt + dwt, |u|? 1, xt observed. For each control law there is a definite cost v(1?t, x) of starting at x, t and using that law till t = 1, expressible as an integral with respect to (a suitable) P?. By restricting attention to a dense set of smooth laws, using Itô's lemma, Kac's theorem, and the maximum principle for parabolic equations, it is possible to calculate sgn vx for a critical class of control laws, then to compare control laws, “solve” the Bellman-Hamilton-Jacobi equation, and thus justify selection of the obvious bang-bang law as optimal. 相似文献
13.
A distance matrix D of order n is symmetric with elements , where dii=0. D is Euclidean when the quantities dij can be generated as the distances between a set of n points, X (n×p), in a Euclidean space of dimension p. The dimensionality of D is defined as the least value of p=rank(X) of any generating X; in general p+1 and p+2 are also acceptable but may include imaginary coordinates, even when D is Euclidean. Basic properties of Euclidean distance matrices are established; in particular, when ρ=rank(D) it is shown that, depending on whether eTD?e is not or is zero, the generating points lie in either p=ρ?1 dimensions, in which case they lie on a hypersphere, or in p=ρ?2 dimensions, in which case they do not. (The notation e is used for a vector all of whose values are one.) When D is non-Euclidean its dimensionality p=r+s will comprise r real and s imaginary columns of X, and (r, s) are invariant for all generating X of minimal rank. Higher-ranking representations can arise only from p+1=(r+1)+s or p+1=r+ (s+1) or p+2=(r+1)+(s+1), so that not only are r, s invariant, but they are both minimal for all admissible representations X. 相似文献
14.
N.J Kalton 《Journal of Functional Analysis》1981,42(3):299-337
We prove a number of results concerning isomorphisms between spaces of the type Lp(X), where X is a separable p-Banach space and 0 < p < 1. Our results imply that the quotient of Lp([0, 1] × [0, 1]) by the subspace of functions depending only on the first variable is not isomorphic to Lp, answering a question of N. T. Peck. More generally if 0 is a sub-σ-algebra of the Borel sets of [0, 1], then , 0) is isomorphic to Lp if and only if Lp([0, 1], B0) is complemented. We also show that Lp has, up to isomorphism, at most one complemented subspace non-isomorphic to Lp and classify completely those spaces X for which . In particular if then or is finite-dimensional. If X has trivial dual and . 相似文献
15.
Hannu Niemi 《Journal of multivariate analysis》1984,15(1):99-123
Necessary and sufficient conditions for an arbitrary q-variate stationary sequence xt, t ∈ , to be deterministic are presented. A characterization of the rank r(x) of xt, t ∈ , and a method to construct the Wold-Cramér decomposition for xt, t ∈ , are given. Subordination of q-variate bounded orthogonally scattered vector measures is considered. 相似文献
16.
Let G be a metric locally compact Abelian group. We prove that the spaces (L1, Lip(α, p)), (L1, lip(α, p)), Lip(α, p) and lip(α, p)~ are isometrically isomorphic, where Lip(α, p) and lip(α, p) denote the Lipschitz spaces defined on G, (L1, A) is the space of multipliers from L1 to A, and lip(α, p)~ denotes the relative completion of lip(α, p). We also show that . 相似文献
17.
John R Bloom 《Journal of Number Theory》1979,11(2):239-256
Let k ? k1 ? … ? K be a Zi-extension. The relations of and is studied, where is a cyclic l-extension. If is another Zi-extension of k, it is shown that for i ? 0, under minimal additional hypotheses. Finally if has a unique totally ramified prime, and XK is cyclic, it is shown that MK can contain at most one Zi-extension with non-zero μ invariant. 相似文献
18.
Kenneth Kramer 《Journal of Number Theory》1985,21(2):204-213
Explicit formulas are given for the quadratic and quartic characters of units of certain quadratic fields in terms of representations by positive definite binary quadratic forms, as conjectured by Leonard and Williams (Pacific J. Math.71 (1977), Rocky Mountain J. Math.9 (1979)), and by Lehmer (J. Reine Angew. Math.268/69 (1974)). For example, if p and a are primes such that p≡1 (mod 8), q≡5 (mod 8) and the Legendre symbol , and if ε is the fundamental unit of (√q), then , where p=a2+16b2 and pk=c2+16qd2 with k odd. 相似文献
19.
The least absolute deviation estimates L(N), from N data points, of the autoregressive constants a = (a1, …, aq)′ for a stationary autoregressive model, are shown to have the property that Nσ(L(N) ? a) converge to zero in probability, for , where the disturbances are i.i.d., attracted to a stable law of index α, 1 ≤ α < 2, and satisfy some other conditions. 相似文献
20.
We study a continuous time growth process on (d?1) associated to the following interacting particle system: initially there is only one simple symmetric continuous time random walk of total jump rate one located at the origin; then, whenever a random walk visits a site still unvisited by any other random walk, it creates a new independent random walk starting from that site. Let us call Pd the law of such a process and S0d(t) the set of sites, visited by all walks by time t. We prove that there exists a bounded, non-empty, convex set , such that for every ε>0, Pd-a.s. eventually in t, the set Sd0(t) is within an ε neighborhood of the set [Cdt], where for we define . Moreover, for d large enough, the set Cd is not a ball under the Euclidean norm. We also show that the empirical density of particles within Sd0(t) converges weakly to a product Poisson measure of parameter one. To cite this article: A.F. Ram??rez, V. Sidoravicius, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 821–826. 相似文献