On Orthogonal Polynomials and the Malliavin Derivative for Levy Stochastic Measures
On Orthogonal Polynomials and the Malliavin Derivative for Levy Stochastic Measures
复制标题
关于Levy随机测度的正交多项式和Malliavin导数
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
G. Nunno
中科院分区：
文献类型：
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作者：
G. Nunno
考虑一般拓扑空间上关于Levy随机测度的随机多项式正交系统。在随机测度是高斯或泊松型的情况下，这个正交系统被证明具有类似于高斯变量的厄米特多项式的性质。本文还讨论了拓扑空间上关于Levy随机测度的随机微分问题。我们引入了一种形式的马利万导数，并提出了一个有效的直接微分公式
We consider an orthogonal system of stochastic polynomials with respect to a Levy stoachastic measure on a general topological space. In the case the stochastic measure is Gaussian or of the Poisson type, this orthogonal system turns out to have properties similar to the ones of the Hermite polynomials of Gaussian variables. In this paper we also deal with stochastic dierentiation with respect to Levy stochastic measures on topological spaces. We introduce a version of the Malliavin derivative and we suggest a direct dierentiation formula which is valid