Generalized functionals of Compound Poisson noise and its applications

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Our general purpose of our research is to determine the structure of random complex system by appealing to the method of reduction ; namely, we construct a system of independent random variables from the given system, which is to be represented by functions of those independent variables. We know two basic systems fitting for our purpose : one is a Gaussian white noise and the other is Poisson noiseA Poisson noise, in particular, a compound Poisson noise requires us to have profound surveys, so that we have obtained their invariances under transformations groups, dualities between the two noises and othersAs a related topic, we have discovered significance of the roles played by the noise with the parameter that comes from the intensity