# Mark Veillette - Boston University

**Starts:**4:00 pm on Thursday, September 16, 2010

**Ends:**5:00 pm on Thursday, September 16, 2010

**Location:**MCS 149

TITLE: The Rosenblatt distribution
ABSTRACT: Fractional Brownian motion is the only Gaussian process which is self-similar and has stationary increments. In this talk, I'll discuss the simplest NON-Gaussian process with these properties, called the Rosenblatt process. I'll begin by motivating this process as a double Wiener-Ito Stochastic integral, and then we will turn to the marginal distribution of the process at time t=1 (called the Rosenblatt distribution). No closed form exists for the PDF, CDF or characteristic function of this distribution, and its moments are not easily obtainable. We will shed some light on these areas by using a representation of the Rosenblatt distribution as an infinite sum of weighted chi-squared distributions. We then develop a technique that allows us to compute with high precision the PDF and CDF of this distribution.