The goal of this U.S.-Croatian cooperative research project between Renming Song of the University of Illinois Urbana-Champaign and Zoran Vondracek of the University of Zagreb is to strengthen the potential theory of Markov processes with jumps. This will be accomplished by bringing together U.S. and Croatian mathematicians to examine five types of problems: 1) potential theory for subordinate killed Brownian motion in a domain; 2) Harnack inequality for Markov processes with jumps; 3) fine properties of the mixture of a Brownian motion and a rotationally invariant stable process; 4) potential theory of non-symmetric stable processes; and 5) Hardy and potential inequalities. Results are expected to lead to a refined theoretical framework for determining mathematical probability. Success would enhance modeling and analysis of various stochastic processes in fields such as physics, operations research, queuing theory, mathematical finance and insurance mathematics.
This mathematics project fulfills the program objective of advancing scientific knowledge by enabling experts in the United States and South Central Europe to combine complementary talents and share research resources in areas of strong mutual interest and competence. Broader impacts include the introduction of U.S. and Croatian graduate students to the international mathematics community through work at partner institutions and direct access to advanced work on jump processes.
