Mathematical Finance and Probability Seminars (Since covid these events are taking place online.)
Gaussian Random Fields: Spectral Measures and Fine Properties
Friday, October 21, 2011 at 03:00pm - 04:00pm
Speaker: Yimin Xiao, Michigan State University
Consider a centered Gaussian random fi eld {X =X(t);tin R^N} with stationary increments and spectral measure ?. There are three interesting cases for the spectral measure:
(i) it is absolutely continuous (the most familiar case is fractional Brownian motion); or
(ii) it is singular and is supported on a fractal set; or
(iii) it is supported on a discrete set.
In all these three cases, the sample function X(t) can either be differentiable almost everywhere or non-differentiable almost everywhere . In this talk we
present some recent results which connect the sample path regularity and fractal properties of a Gaussian random eld with the asymptotic properties of ?.
Speaker: Yimin Xiao, Michigan State University