Seminar at SMU Delhi

Subordinated stochastic processes (also called time-changed processes) $X(T (t))$ are obtained by time changing a parent process $X(t)$ with a positive non-decreasing stochastic process $T (t).$ The process $X(T (t))$ is said to be subordinated to the process $X(t)$ and the subordinator $T (t)$ is called the directing process. Subordinated processes have interesting probabilistic proper- ties and have applications in finance, economics, statistical physics and fractional calculus. The aim of this talk is to introduce the concept of time-changed processes and to discuss the application of these processes in different fields. The idea is also to introduce different time-changed processes that have been used in literature in recent years.