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<p>The main purpose of this paper is to derive a general new structure of generalized noise analysis by using the interacting Fock space techniques. First, we start with a detailed construction of the interacting Fock space which serves to obtain the quantum decomposition of such random variables as sums of creation, annihilation and preservation operators. Next, we determine the distribution of the generalized noise operator and as an application of the general rules, we show that the distribution of the interacting noise operator on the multiple interacting Fock space with a suitable test function is the arcsine law.</p>

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Constructive of the Generalized Noise Process Based on Interacting Fock Spaces

  • 期刊论文

  • 发表日期：

    2025年2月9日

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  • Anis Riahi,
  • Mohamed Rhaima,
  • Hamza Ghoudi

摘要

The main purpose of this paper is to derive a general new structure of generalized noise analysis by using the interacting Fock space techniques. First, we start with a detailed construction of the interacting Fock space which serves to obtain the quantum decomposition of such random variables as sums of creation, annihilation and preservation operators. Next, we determine the distribution of the generalized noise operator and as an application of the general rules, we show that the distribution of the interacting noise operator on the multiple interacting Fock space with a suitable test function is the arcsine law.