Let（S）L<sup>2</sup>（S’（IR）,μ）（S）<sup>*</sup> be the Gel’fand triple over the white noise space （S’（IR）,μ）.Let（e<sub>n</sub>,n≥0）be the ONB of L<sup>2</s...Let（S）L<sup>2</sup>（S’（IR）,μ）（S）<sup>*</sup> be the Gel’fand triple over the white noise space （S’（IR）,μ）.Let（e<sub>n</sub>,n≥0）be the ONB of L<sup>2</sup>（IR）consisting of the eigenfunctions of the s.a. operator-（d/（dt））<sup>2</sup>+1+t<sup>2</sup>.In this paper the Euler operator △<sub>E</sub> is defined as the sum ∑<sub>i</sub>【,e<sub>i</sub>)<sub>i</sub>, where <sub>i</sub> stands for the differential operator D<sub>ei</sub>.It is shown that △<sub>E</sub> is the infinitesimal gen- erator of the semigroup（T<sub>t</sub>）,where(T<sub>t</sub>)（x）=（e<sup>t</sup>x）for ∈（S）.Similarly to the finite dimensional case,the λ-order homogeneous test functionals are characterized by the Euler equa- tion:△<sub>E</sub>=λ.Via this characterization the λ-order homogeneous Hida distributions are defined and their properties are worked out.展开更多
In this paper, the generalized local time of the indefinite Wiener integral Xt is discussed through white noise approach, which means to regard the local time as a Hida distribution. Moreover, similar result is also o...In this paper, the generalized local time of the indefinite Wiener integral Xt is discussed through white noise approach, which means to regard the local time as a Hida distribution. Moreover, similar result is also obtained in case of two independent Brownian motions by using the similar approach.展开更多
In this paper, we present a new idea to study the stochastic current within the canonical framework of white noise analysis. We define Wick-type stochastic current by using Wick integral with respect to Brownian motio...In this paper, we present a new idea to study the stochastic current within the canonical framework of white noise analysis. We define Wick-type stochastic current by using Wick integral with respect to Brownian motion, firstly. Moreover, we prove that the Brownian stochastic current is considered as a Hida distribution in terms of white noise approach and S-transform.展开更多
基金Supported by the National Natural Science Foundation of China
文摘Let（S）L<sup>2</sup>（S’（IR）,μ）（S）<sup>*</sup> be the Gel’fand triple over the white noise space （S’（IR）,μ）.Let（e<sub>n</sub>,n≥0）be the ONB of L<sup>2</sup>（IR）consisting of the eigenfunctions of the s.a. operator-（d/（dt））<sup>2</sup>+1+t<sup>2</sup>.In this paper the Euler operator △<sub>E</sub> is defined as the sum ∑<sub>i</sub>【,e<sub>i</sub>)<sub>i</sub>, where <sub>i</sub> stands for the differential operator D<sub>ei</sub>.It is shown that △<sub>E</sub> is the infinitesimal gen- erator of the semigroup（T<sub>t</sub>）,where(T<sub>t</sub>)（x）=（e<sup>t</sup>x）for ∈（S）.Similarly to the finite dimensional case,the λ-order homogeneous test functionals are characterized by the Euler equa- tion:△<sub>E</sub>=λ.Via this characterization the λ-order homogeneous Hida distributions are defined and their properties are worked out.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1106103230973586)
文摘In this paper, the generalized local time of the indefinite Wiener integral Xt is discussed through white noise approach, which means to regard the local time as a Hida distribution. Moreover, similar result is also obtained in case of two independent Brownian motions by using the similar approach.
基金Supported by National Natural Science Foundation of China(Grant No.11061032)Colleges and Universities Scientific Research Funds Project Plan of Gansu Province for Postgraduate Tutor(Grant No.1205-07)Colleges and Universities Fundamental Research Funds Project of Gansu Province(2012)
文摘In this paper, we present a new idea to study the stochastic current within the canonical framework of white noise analysis. We define Wick-type stochastic current by using Wick integral with respect to Brownian motion, firstly. Moreover, we prove that the Brownian stochastic current is considered as a Hida distribution in terms of white noise approach and S-transform.
