B.L.S. Prakasa Rao
CR Rao Advanced Institute, Hyderabad, India
16 septembre 2016 de 16 h 00 à 18 h 00 (heure de Montréal/HNE) Sur place
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.
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