## STA 290 Seminar: Prakasa Rao (U Hyderabad, India)

### Statistics Seminar: STA 290

FRIDAY, May 16th 2014 at 3:10pm, MSB 1147 (Colloquium Room)

Speaker: **Professor B.L.S. Prakasa Rao**

Ramanujan Chair Professor

CR RAO Advanced Institute of Mathematics, Statistics & Computer Science

University of Hyderabad Campus, India

Title: **"****Statistical inference for fractional diffusion processes"**

Abstract: There are some time series which exhibit long-range dependence as noticed by Hurst in his investigations of river water levels along Nile river. Long-range dependence is connected with the concept of self-similarity in that increments of a self-similar process with stationary increments exhibit long-range dependence under some conditions. Fractional Brownian motion is an example of such a process. We discuss statistical inference for stochastic processes modeled by stochastic differential equations driven by a fractional Brownian motion. These processes are termed as fractional diffusion processes. Since fractional Brownian motion is not a semimartingale, it is not possible to extend the notion of a stochastic integral with respect to a fractional Brownian motion following the ideas of Ito integration. There are other methods of extending integration with respect to a fractional Brownian motion. Suppose a complete path of a fractional diffusion process is observed over a finite time interval. We will present some results on inference for such processes. Some recent work on change-point problems will be discussed.