Pascal white noise calculus
Pascal white noise calculus
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DOI：
10.1080/17442500902919603
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发表时间：
2009-06
期刊：
影响因子：
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通讯作者：
A. Barhoumi;H. Ouerdiane;A. Riahi
中科院分区：
文献类型：
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作者：
A. Barhoumi;H. Ouerdiane;A. Riahi
本文研究了具有负二项分布边缘的Lévy过程的白噪声分析。用一个适当的分布空间ℰ‘来描述关于Pascal白噪声测度ΛNb的二次可积泛函的希尔伯特空间的结构。构造的分解被用来定义测试函数和广义函数的核三元组，其中θ是满足一定条件的杨函数。利用𝒮变换和符号变换σNb，证明了关于Pascal型白噪声分布、白噪声检验函数和白噪声算子的一般刻画定理.作为应用，给出了一些量子随机微分方程解的实例，并着重介绍了Wick演算。
In this paper white noise analysis with respect to the Lévy process with negative binomial distributed marginals is investigated. An appropriate space of distributions, ℰ ′, is used to describe the structure of the Hilbert space of quadratic integrable functionals with respect to the Pascal white noise measure ΛNB. The constructed decomposition is used to define a nuclear triple of test and generalized functions, where θ is a Young function satisfying some suitable conditions. By using the 𝒮-transform and the symbol transform σNB, a general characterization theorems are proven for Pascal white noise distributions, white noise test functions and white noise operators in terms of analytical functions with growth condition of exponential type. As application, some quantum stochastic differential equations are solved with special emphasis on Wick calculus.