Quebec Mathematical Sciences Colloquium

September 16, 2016 from 16:00 to 18:00 (Montreal/Miami time) On location

Statistical Inference for fractional diffusion processes

Colloquium presented by B.L.S. Prakasa Rao (CR Rao Advanced Institute, Hyderabad, India)

There are some time series which exhibit long­range dependence as noticed by Hurst in his investigations of river water levels along Nile river. Long­range dependence is connected with the concept of self­similarity in that increments of a self­similar process with stationary increments exhibit long­range 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 problems for such processes.

Address

Université Concordia, Library Building, 1400 de Maisonneuve O., room LB­921.04