| A shot noise model is a stochastic process composed of a superposition of "shot" effects, given by a response function, which occur at random times of a point process. Attached to each timepoint is a measurement called a "mark" involved in the response function. This type of stochastic process is used in telecommunications, finance, insurance, reliability, and diverse other fields, for modeling variables such as total electric current, number of busy connections, number of workers on compensation insurance, size of an immigration-death population process, and the like.;In this dissertation, shot noise processes are studied on cluster point processes, involving two types of marks. One type of mark is related to the cluster, and the other is associated with a cluster member. In the present development, the model of shot noise on cluster processes with cluster marks is treated under general assumptions, and significant extension of previous results are obtained.;The cluster shot noise with cluster marks is characterized by the probability generating functional, the characteristic functional (and characteristic function), and the mean, variance and covariance functions. The general results obtained are specialized to the broad class of shot noise on a Neyman-Scott type cluster process with cluster marks, and several exact results are obtained and applied to particular cases of interest.;This dissertation also addresses some nonstandard properties of a shot noise process, such as heavy tail and long range dependence.;Besides exact results, some asymptotic results are developed that indicate the conditions under which the normalized shot noise converges to some limit, in the general case of arbitrary Poisson cluster models, including heavy-tail behavior.;Additionally, some selected further results on shot noise models are obtained for regenerative-type shot noise processes and shot noise on arbitrary renewal type point processes. |
