共查询到20条相似文献,搜索用时 578 毫秒
1.
William E Strawderman 《Journal of multivariate analysis》1974,4(3):255-264
Families of minimax estimators are found for the location parameters of a p-variate distribution of the form , where G(·) is a known c.d.f. on (0, ∞), p ≥ 3 and the loss is sum of squared errors. The estimators are of the form where 0 ≤ a ≤ 2, r(X′X) is nondecreasing, and is nonincreasing. Generalized Bayes minimax estimators are found for certain G(·)'s. 相似文献
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《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1998,326(5):595-599
This Note presents a construction of a solution for the nonlinear stochastic differential equation Xt = X0 + ∫0t [u0(X0)|Xs]ds, t ≥ 0. The random variable X0 with values in and the function u0 are given. We denote by Pt the probability distribution of Xt and u(x, t) = [u0(X0)|Xt = x]. We prove that (Pt, u(·, t), t ≥ 0) is a weak solution for system of conservation law arising in adhesion particle dynamics. 相似文献
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Malcolm R. Adams 《Journal of Functional Analysis》1983,52(3):420-441
Let Q be a self-adjoint, classical, zeroth order pseudodifferential operator on a compact manifold X with a fixed smooth measure dx. We use microlocal techniques to study the spectrum and spectral family, {ES}S∈ as a bounded operator on L2(X, dx).Using theorems of Weyl (Rend. Circ. Mat. Palermo, 27 (1909), 373–392) and Kato (“Perturbation Theory for Linear Operators,” Springer-Verlag, 1976) on spectra of perturbed operators we observe that the essential spectrum and the absolutely continuous spectrum of Q are determined by a finite number of terms in the symbol expansion. In particular SpecESSQ = range(q(x, ξ)) where q is the principal symbol of Q. Turning the attention to the spectral family {ES}S∈, it is shown that if is considered as a distribution on ×X×X it is in fact a Lagrangian distribution near the set where (s, x, y, σ, ξ,η) are coordinates on T1(×X×X) induced by the coordinates (s, x, y) on ×X×X. This leads to an easy proof that is a pseudodifferential operator if ?∈C∞() and to some results on the microlocal character of Es. Finally, a look at the wavefront set of leads to a conjecture about the existence of absolutely continuous spectrum in terms of a condition on q(x, ξ). 相似文献
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F Thaine 《Journal of Number Theory》1982,15(3):304-317
We study properties of the polynomials φk(X) which appear in the formal development Πk ? 0n (a + bXk)rk = Σk ≥ 0φk(X) ar ? kbk, where rk ∈ and r = Σrk. this permits us to obtain the coefficients of all cyclotomic polynomials. Then we use these properties to expand the cyclotomic numbers Gr(ξ) = Πk = 1p ? 1 (a + bξk)kr, where p is a prime, ξ is a primitive pth root of 1, a, b ∈ and 1 ≤ r ≤ p ? 3, modulo powers of ξ ? 1 (until (ξ ? 1)2(p ? 1) ? r). This gives more information than the usual logarithmic derivative. Suppose that . Let . We prove that Gr(ξ) ≡ cp mod p(ξ ? 1)2 for some c ∈ , if and only if Σk = 1p ? 1kp ? 2 ? rmk ≡ 0 (mod p). We hope to show in this work that this result is useful in the study of the first case of Fermat's last theorem. 相似文献
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Michel Las Vergnas 《Discrete Mathematics》1978,23(3):241-255
We prove the following theorem: Let G be a graph with vertex-set V and ?, g be two integer-valued functions defined on V such that for all x ∈ V. Then G contains a factor F such that for all x ∈ V if and only if for every subset X of V, is at least equal to the number of connected components C of G[V ? X] such that either C = {x} and g(x) = 1, or |C| is odd ?3 and for all x ∈ C. Applications are given to certain combinatorial geometries associated with factors of graphs. 相似文献
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Let Z = {Z0, Z1, Z2,…} be a martingale, with difference sequence X0 = Z0, Xi = Zi ? Zi ? 1, i ≥ 1. The principal purpose of this paper is to prove that the best constant in the inequality λP(supi |Xi| ≥ λ) ≤ C supiE |Zi|, for λ > 0, is C = (log 2)?1. If Z is finite of length n, it is proved that the best constant is . The analogous best constant Cn(z) when Z0 ≡ z is also determined. For these finite cases, examples of martingales attaining equality are constructed. The results follow from an explicit determination of the quantity Gn(z, E) = supzP(maxi=1,…,n |Xi| ≥ 1), the supremum being taken over all martingales Z with Z0 ≡ z and E|Zn| = E. The expression for Gn(z,E) is derived by induction, using methods from the theory of moments. 相似文献
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Robert Chen 《Journal of multivariate analysis》1978,8(2):328-333
Let {Xn}n≥1 be a sequence of independent and identically distributed random variables. For each integer n ≥ 1 and positive constants r, t, and ?, let Sn = Σj=1nXj and . In this paper, we prove that (1) lim?→0+?α(r?1)E{N∞(r, t, ?)} = K(r, t) if E(X1) = 0, Var(X1) = 1, and E(| X1 |t) < ∞, where 2 ≤ t < 2r ≤ 2t, , and ; (2) if 2 < t < 4, E(X1) = 0, Var(X1) > 0, and E(|X1|t) < ∞, where G(t, ?) = E{N∞(t, t, ?)} = Σn=1∞nt?2P{| Sn | > ?n} → ∞ as ? → 0+ and , i.e., H(t, ?) goes to infinity much faster than G(t, ?) as ? → 0+ if 2 < t < 4, E(X1) = 0, Var(X1) > 0, and E(| X1 |t) < ∞. Our results provide us with a much better and deeper understanding of the tail probability of a distribution. 相似文献
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R.S. Singh 《Journal of multivariate analysis》1976,6(2):338-342
Let Xj = (X1j ,…, Xpj), j = 1,…, n be n independent random vectors. For x = (x1 ,…, xp) in Rp and for α in [0, 1], let Fj(x) = αI(X1j < x1 ,…, Xpj < xp) + (1 ? α) I(X1j ≤ x1 ,…, Xpj ≤ xp), where I(A) is the indicator random variable of the event A. Let Fj(x) = E(Fj(x)) and Dn = supx, α max1 ≤ N ≤ n |Σ0n(Fj(x) ? Fj(x))|. It is shown that P[Dn ≥ L] < 4pL exp{?2(L2n?1 ? 1)} for each positive integer n and for all L2 ≥ n; and, as n → ∞, with probability one. 相似文献
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Simeon M. Berman 《Journal of multivariate analysis》1978,8(1):30-44
Let R(s, t) be a continuous, nonnegative, real valued function on a ≤ s ≤ t ≤ b. Suppose , , and in the interior of the domain. Then the extension of R to a symmetric function on [a, b] × [a, b] is a covariance function. Such a covariance is called biconvex. Let X(t) be a Gaussian process with mean 0 and biconvex covariance. X has a representation as a sum of simple moving averages of white noises on the line and plane. The germ field of X at every point t is generated by X(t) alone. X is locally nondeterministic. Under an additional assumption involving the partial derivatives of R near the diagonal, the local time of the sample function exists and is jointly continuous almost surely, so that the sample function is nowhere differentiable. 相似文献
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Hui-Hsiung Kuo 《Journal of Functional Analysis》1976,21(1):63-75
Some parallel results of Gross' paper (Potential theory on Hilbert space, J. Functional Analysis1 (1967), 123–181) are obtained for Uhlenbeck-Ornstein process U(t) in an abstract Wiener space (H, B, i). Generalized number operator is defined by f(x) = ?lim∈←0{E[f((τ∈ξ))] ? f(x)}/E[τ∈ξ, where τx? is the first exit time of U(t) starting at x from the ball of radius ? with center x. It is shown that f(x) = ?trace D2f(x)+〈Df(x),x〉 for a large class of functions f. Let rt(x, dy) be the transition probabilities of U(t). The λ-potential Gλf, λ > 0, and normalized potential Rf of f are defined by Gλf(X) = ∫0∞e?λtrtf(x) dt and Rf(x) = ∫0∞ [rtf(x) ? rtf(0)] dt. It is shown that if f is a bounded Lip-1 function then trace D2Gλf(x) ? 〈DGλf(x), x〉 = ?f(x) + λGλf(x) and trace D2Rf(x) ? 〈DRf(x), x〉 = ?f(x) + ∫Bf(y)p1(dy), where p1 is the Wiener measure in B with parameter 1. Some approximation theorems are also proved. 相似文献
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N.R. Mohan 《Stochastic Processes and their Applications》1976,4(2):157-165
Let X1, X2, … be a sequence of independent and identically distributed random variables with mean zero such that the common distribution function belongs to the domain of attraction of a stable law Gα,β with 1<α<2 and β=1 or α=2. If Sn=X1+…Xn and N(ξ)=min{k:Sk>ξ}, ξ>0, then it is shown that , 0<t<1, converges weakly under the Skorohod J1-topology to a stable subordinator of index , where B1(n) depends on the norming constant for Sn. 相似文献
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Alain Escassut 《Journal of Number Theory》1983,16(3):395-402
Let (K, ∥ · ∥) be a valued transcendence degree 1 extension of p. An element x ∈ K transcendental over p is said to have order ≤a (a > 0) if there exists Cx > 0 such that every polynomial P(X) ∈ p [X] satisfies when ∥ · ∥ is the Gauss norm on p[X]. No x ∈ p can have order ≤α if α < 1 but we construct some x ∈ p with order ≤ 1. Furthermore, we prove order ≤α is stable by algebraic extension. 相似文献
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Palle E.T Jørgensen 《Journal of Functional Analysis》1975,20(2):105-135
In this paper we apply the theory of second-order partial differential operators with nonnegative characteristic form to representations of Lie groups. We are concerned with a continuous representation U of a Lie group G in a Banach space . Let be the enveloping algebra of G, and let dU be the infinitesimal homomorphism of into operators with the Gårding vectors as a common invariant domain. We study elements in of the form with the Xj,'s in the Lie algebra .If the elements X0, X1,…, Xr generate as a Lie algebra then we show that the space of C∞-vectors for U is precisely equal to the C∞-vectors for the closure . This result is applied to obtain estimates for differential operators.The operator is the infinitesimal generator of a strongly continuous semigroup of operators in . If X0 = 0 we show that this semigroup can be analytically continued to complex time ζ with Re ζ > 0. The generalized heat kernels of these semigroups are computed. A space of rapidly decreasing functions on G is introduced in order to treat the heat kernels.For unitary representations we show essential self-adjointness of all operators with X0 in the real linear span of the Xj's. An application to quantum field theory is given.Finally, the new characterization of the C∞-vectors is applied to a construction of a counterexample to a conjecture on exponentiation of operator Lie algebras.Our results on semigroups of exponential growth, and on the space of C∞ vectors for a group representation can be viewed as generalizations of various results due to Nelson-Stinespring [18], and Poulsen [19], who prove essential self-adjointness and a priori estimates, respectively, for the sum of the squares of elements in a basis for (the Laplace operator). The work of Hörmander [11] and Bony [3] on degenerate-elliptic (hypoelliptic) operators supplies the technical basis for this generalization. The important feature is that elliptic regularity is too crude a tool for controlling commutators. With the aid of the above-mentioned hypoellipticity results we are able to “control” the (finite dimensional) Lie algebra generated by a given set of differential operators. 相似文献