Date of Award
Doctor of Philosophy (PhD)
The aim of the dissertation is to establish the weak convergence of mean-field interacting particle systems driven by Poisson random measures and semimartingales. The limit of the stochastic systems is identified by the use of martingale problems and Picard iteration schemes. The interacting systems driven by Poisson random measures are shown to be stable with respect to the coefficients of the system as well as the driving terms. The same results can be achieved when a random interaction term independent of the driving terms is introduced into the coefficients of the system. Equations driven by semimartingales do not neccesarily possess the Markov property. In such a case martingale problems are no longer available, and hence identification of the limit is established by suitable approximation schemes.
Paslaski, George William, "Weak Convergence of Interacting Stochastic Systems." (1997). LSU Historical Dissertations and Theses. 6589.