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排序方式: 共有6905条查询结果,搜索用时 15 毫秒
951.
In this paper, problems related to the approximation of a holomorphic function f on a compact subset E of the complex plane C by rational functions from the class of all rational functions of order (n,m) are considered. Let ρ
n,m
= ρ
n,m
(f;E) be the distance of f in the uniform metric on E from the class . We obtain results characterizing the rate of convergence to zero of the sequence of the best rational approximation { ρ
n,m(n)
}
n=0
∞
, m(n)/n
→
θ
∈ (0,1] as n
→
∞ . In particular, we give an upper estimate for the liminf
n →∞
ρ
n,m(n)
1/(n+m(n))
in terms of the solution to a certain minimum energy problem with respect to the logarithmic potential. The proofs of the
results obtained are based on the methods of the theory of Hankel operators.
June 16, 1997. Date revised: December 1, 1997. Date accepted: December 1, 1997. Communicated by Ronald A. DeVore. 相似文献
952.
The purpose of this paper is to study certain variational principles and Sobolev-type estimates for the approximation order
resulting from using strictly positive definite kernels to do generalized Hermite interpolation on a closed (i.e., no boundary),
compact, connected, orientable, m -dimensional C
∞
Riemannian manifold , with C
∞
metric g
ij
. The rate of approximation can be more fully analyzed with rates of approximation given in terms of Sobolev norms. Estimates
on the rate of convergence for generalized Hermite and other distributional interpolants can be obtained in certain circumstances
and, finally, the constants appearing in the approximation order inequalities are explicit. Our focus in this paper will be
on approximation rates in the cases of the circle, other tori, and the 2 -sphere.
April 10, 1996. Dates revised: March 26, 1997; August 26, 1997. Date accepted: September 12, 1997. Communicated by Ronald
A. DeVore. 相似文献
953.
The dependence of the Whittaker function M
κ, μ
(z) on the parameter κ is considered. A convergent expansion in ascending powers and an asymptotic expansion in descending powers of κ are discussed. Some properties of the coefficients of the convergent expansion are shown.
February 14, 1997. Date revised: March 5, 1998. Date accepted: March 19, 1998. 相似文献
954.
Stochastic Ising and voter models on ℤ
d
are natural examples of Markov processes with compact state spaces. When the initial state is chosen uniformly at random,
can it happen that the distribution at time t has multiple (subsequence) limits as t→∞? Yes for the d = 1 Voter Model with Random Rates (VMRR) – which is the same as a d = 1 rate-disordered stochastic Ising model at zero temperature – if the disorder distribution is heavy-tailed. No (at least in a weak sense) for the VMRR when the tail is light or d≥ 2. These results are based on an analysis of the “localization” properties of Random Walks with Random Rates.
Received: 10 August 1998 相似文献
955.
We study some discrete isoperimetric and Poincaré-type inequalities for product probability measures μ
n
on the discrete cube {0, 1}
n
and on the lattice Z
n
. In particular we prove sharp lower estimates for the product measures of boundaries of arbitrary sets in the discrete cube.
More generally, we characterize those probability distributions μ on Z which satisfy these inequalities on Z
n
. The class of these distributions can be described by a certain class of monotone transforms of the two-sided exponential
measure. A similar characterization of distributions on R which satisfy Poincaré inequalities on the class of convex functions is proved in terms of variances of suprema of linear
processes.
Received: 30 April 1997 / Revised version: 5 June 1998 相似文献
956.
In this paper we study the well-posedness and regularity of the adapted solutions to a class of linear, degenerate backward stochastic partial differential equations (BSPDE, for short). We establish new
a priori estimates for the adapted solutions to BSPDEs in a general setting, based on which the existence, uniqueness, and regularity
of adapted solutions are obtained. Also, we prove some comparison theorems and discuss their possible applications in mathematical
finance.
Received: 24 September 1997 / Revised version: 3 June 1998 相似文献
957.
Shige Peng 《Probability Theory and Related Fields》1999,113(4):473-499
We have obtained the following limit theorem: if a sequence of RCLL supersolutions of a backward stochastic differential
equations (BSDE) converges monotonically up to (y
t
) with E[sup
t
|y
t
|2] < ∞, then (y
t
) itself is a RCLL supersolution of the same BSDE (Theorem 2.4 and 3.6).
We apply this result to the following two problems: 1) nonlinear Doob–Meyer Decomposition Theorem. 2) the smallest supersolution
of a BSDE with constraints on the solution (y, z). The constraints may be non convex with respect to (y, z) and may be only measurable with respect to the time variable t. this result may be applied to the pricing of hedging contingent claims with constrained portfolios and/or wealth processes.
Received: 3 June 1997 / Revised version: 18 January 1998 相似文献
958.
Pao-Liu Chow Ildar A. Ibragimov Rafail Z. Khasminskii 《Probability Theory and Related Fields》1999,113(3):421-441
For linear partial differential equations, some inverse source problems are treated statistically based on nonparametric
estimation ideas. By observing the solution in a small Gaussian white noise, the kernel type of estimators is used to estimate
the unknown source function and its partial derivatives.. It is proved that such estimators are consistent as the noise intensity
tends to zero. Depending on the principal part of the differential operator, the optimal asymptotic rate of convergence is
ascertained within a wide class of risk functions in a minimax sense.
Received: 5 May 1997 / Revised version: 18 June 1998 相似文献
959.
960.
We consider the existence of distributional (or L
2
) solutions of the matrix refinement equation
where P is an r×r matrix with trigonometric polynomial entries.
One of the main results of this paper is that the above matrix refinement equation has a compactly supported distributional
solution if and only if the matrix P
(0) has an eigenvalue of the form 2
n
, . A characterization of the existence of L
2
-solutions of the above matrix refinement equation in terms of the mask is also given.
A concept of L
2
-weak stability of a (finite) sequence of function vectors is introduced. In the case when the function vectors are solutions
of a matrix refinement equation, we characterize this weak stability in terms of the mask.
August 1, 1996. Date revised: July 28, 1997. Date accepted: August 12, 1997. 相似文献