Elenco seminari del ciclo di seminari
“AN INTRODUCTION TO STOCHASTIC CALCULUS FOR JUMP PROCESSES”

The objective of this 10-hour PhD course is to provide an introduction to stochastic calculus for jump processes. Starting from the main definitions and results of discontinuous stochastic processes theory, we introduce the stochastic integral with respect to finite variation processes and we investigate its main properties. Moreover, we study stochastic differential equations driven by jump processes, showing an existence and uniqueness result. Finally, we present the Doléans-Dade exponential and we study the martingale property of the stochastic integral.