A Relation Between Permanental Process And General Stochastic Process

This article discusses a class of special stochastic processes which is calledPermanental processes.Permanental processes can be viewed as a generalisationof squared centered Gaussian processes.The beginning of this article elaborated the background of the research andthe current status of the problem, and to introduce the main work of this paper, the theoretical and practical significance of this paper. In the first chapter, weintroduce the random processes and the Laplace transform briefly, give the defini-tion of Permanental processes form the Laplace transform of the random process, take the advantage of the Gaussian squared process to confirm the β index ofPermanental processes and give a accurate expression of β Permanental processand Permanental process. In chapter2, some properties and other forms of Per-manental processes were given, and we proved the existence and continuity of theβ Permanental process and Permanental processes. In chapter3, we discusses theconnection between Permanental process and the general processes, and exploredthe relationship among Permanental process, Le′vy processes, Markov processesand general random process. At the end of the paper, we studied a class ofspecial Permanental process by using the M matrix of nature, that is infinitelydivisible Permanental process.