Seminarium:
Teoria prawdopodobieństwa i modelowanie stochastyczne
Osoba referująca:
Tomasz Rolski (Uniwersytet Wrocławski)
Data:
czwartek, 19. Maj 2022 - 12:15
Sala:
602
Opis:
We consider a family of sup-functionals of (drifted) fractional Brownian motion
with Hurst parameter H. This family includes, but is not limited to: expected value
of the supremum, expected workload, Wills functional, and Piterbarg-Pickands constant.
Explicit formulas for the derivatives of these functionals as functions of Hurst parameter
evaluated at H = 1/2 are established.
In order to derive these formulas, we develop the concept of derivatives of fractional alpha-stable
fields introduced by Stoev & Taqqu (2004) and
propose Paley-Wiener-Zygmund representation of fractional Brownian motion.
The talk is based on joint work with Krzysztof Bisewski and Krzysztof Debicki