Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Speaker:
Dr. Yi Shen,University of Waterloo, Canada
Inviter:
Shunlong Luo
Title:
Location of Path Supremum of Stationary Increment Processes
Time & Venue:
2015.7.8 17:00-18:00 N602
Abstract:
We discuss the distribution of the path supremum over a compact interval of stochastic processes with stationary increments. We start by the most general case and derive structural results for the location of the path supremum, including absolute continuity, a universal upper-bound for the density function, constraints on the total variation of the density function, etc. Then we consider the special case of self-similar processes with stationary increments, and obtain a spectral-type representation for the density function, together with stronger continuity and upper-bound results. Finally we further restrict our attention to self-similar Levy processes, and show that in this case the distribution of path supremum belongs to a simple family of known distributions. This talk is partially based on joint works with Gennady Samorodnitsky.
Appendix：
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