For weighted approximation in Lp-norm,we determine strongly asymptotic orders for the average errors of both function approximation and derivative approximation by the Bernstein operators sequence on the r-fold integr...For weighted approximation in Lp-norm,we determine strongly asymptotic orders for the average errors of both function approximation and derivative approximation by the Bernstein operators sequence on the r-fold integrated Wiener space.展开更多
We introduce anticipating quadrant and symmetric integrals in the plane, and establish the associated chain rules which are the same as the deterministic ones. In particular, we deduce the relation between quadrant in...We introduce anticipating quadrant and symmetric integrals in the plane, and establish the associated chain rules which are the same as the deterministic ones. In particular, we deduce the relation between quadrant integrals, symmetric integral, and Skorohod integral with respect to two-parameter Wiener processes.展开更多
The purpose of this paper is to investigate the behavior of a Wiener integral along the curve C of the scale factor ρ > 0 for the Wiener integral ∫C0[0,T]F(ρx)dm(x) about the function defined on the Wiener space...The purpose of this paper is to investigate the behavior of a Wiener integral along the curve C of the scale factor ρ > 0 for the Wiener integral ∫C0[0,T]F(ρx)dm(x) about the function defined on the Wiener space C0[0,T], where θ(t,u) is a Fourier-Stieltjes transform of a complex Borel measure.展开更多
The purpose of this paper is to investigate the behavior of a scale factor for Wiener integrals about the unbounded function , where {a1,a2,...,an} is an orthonormal set of elements in L2[0,T] on the Wiener space C0[0...The purpose of this paper is to investigate the behavior of a scale factor for Wiener integrals about the unbounded function , where {a1,a2,...,an} is an orthonormal set of elements in L2[0,T] on the Wiener space C0[0,T].展开更多
For the weighted approximation in Lp-norm,the authors determine the weakly asymptotic order for the p-average errors of the sequence of Hermite interpolation based on the Chebyshev nodes on the 1-fold integrated Wiene...For the weighted approximation in Lp-norm,the authors determine the weakly asymptotic order for the p-average errors of the sequence of Hermite interpolation based on the Chebyshev nodes on the 1-fold integrated Wiener space.By this result,it is known that in the sense of information-based complexity,if permissible information functionals are Hermite data,then the p-average errors of this sequence are weakly equivalent to those of the corresponding sequence of the minimal p-average radius of nonadaptive information.展开更多
Suppose β1 〉 α1 ≥ 0, β2 〉 α2 ≥ 0 and （k,j） ∈ R^2. In this paper, we mainly investigate the mapping properties of the operator Tα,βf（x,y,z）=∫Q^2f（x-t,y-s,z-t^ks^j）e^-2πit-β1s-β2t^-1-α1s^-1-α2 dtd...Suppose β1 〉 α1 ≥ 0, β2 〉 α2 ≥ 0 and （k,j） ∈ R^2. In this paper, we mainly investigate the mapping properties of the operator Tα,βf（x,y,z）=∫Q^2f（x-t,y-s,z-t^ks^j）e^-2πit-β1s-β2t^-1-α1s^-1-α2 dtds on modulation spaces, where Q^2 = [0, 1] × [0, 1] is the unit square in two dimensions.展开更多
文摘For weighted approximation in Lp-norm,we determine strongly asymptotic orders for the average errors of both function approximation and derivative approximation by the Bernstein operators sequence on the r-fold integrated Wiener space.
文摘We introduce anticipating quadrant and symmetric integrals in the plane, and establish the associated chain rules which are the same as the deterministic ones. In particular, we deduce the relation between quadrant integrals, symmetric integral, and Skorohod integral with respect to two-parameter Wiener processes.
文摘The purpose of this paper is to investigate the behavior of a Wiener integral along the curve C of the scale factor ρ > 0 for the Wiener integral ∫C0[0,T]F(ρx)dm(x) about the function defined on the Wiener space C0[0,T], where θ(t,u) is a Fourier-Stieltjes transform of a complex Borel measure.
文摘The purpose of this paper is to investigate the behavior of a scale factor for Wiener integrals about the unbounded function , where {a1,a2,...,an} is an orthonormal set of elements in L2[0,T] on the Wiener space C0[0,T].
文摘For the weighted approximation in Lp-norm,the authors determine the weakly asymptotic order for the p-average errors of the sequence of Hermite interpolation based on the Chebyshev nodes on the 1-fold integrated Wiener space.By this result,it is known that in the sense of information-based complexity,if permissible information functionals are Hermite data,then the p-average errors of this sequence are weakly equivalent to those of the corresponding sequence of the minimal p-average radius of nonadaptive information.
基金Supported by NNSF(Grant Nos.11201003 and 11771223)University NSR Project of Anhui Province(Grant Nos.KJ2017ZD27 and KJ2015A117)
文摘Suppose β1 〉 α1 ≥ 0, β2 〉 α2 ≥ 0 and （k,j） ∈ R^2. In this paper, we mainly investigate the mapping properties of the operator Tα,βf（x,y,z）=∫Q^2f（x-t,y-s,z-t^ks^j）e^-2πit-β1s-β2t^-1-α1s^-1-α2 dtds on modulation spaces, where Q^2 = [0, 1] × [0, 1] is the unit square in two dimensions.
