Date of Award
1997
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematics
First Advisor
P. Sundar
Abstract
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.
Recommended Citation
Paslaski, George William, "Weak Convergence of Interacting Stochastic Systems." (1997). LSU Historical Dissertations and Theses. 6589.
https://repository.lsu.edu/gradschool_disstheses/6589
ISBN
9780591724097
Pages
141
DOI
10.31390/gradschool_disstheses.6589