Infinite-Dimensional Linear Stochastic Systems with Random Coefficients and Local Interactions

Abstract: In this thesis some results for a model that is a merge between the random coefficient autoregressive model of order one and a stochastic process with local interaction in time and space are presented. The first part of the thesis deals with some result from the random coefficient model. The second part of this thesis deals with the random coefficient model with local interaction. Results such as expectation, variance bounds and some covariance results are presented.