Levy Processes

Lévy processes are the continuous-time analogues of random walks, and include Brownian motion, compound Poisson processes, and square-integrable pure-jump martingales with many small jumps. In this course we will develop the basic theory of general Lévy processes and subordinators, and discuss topics including local time, excursions, and fluctuations. Time permitting we will finish with selected applications which are of mutual interest to the instructor and students enrolled in the class. Prerequisite: APMA 2640 or equivalent.