Pochodna funkcjonałów typu supremum dla ułamkowego ruchu Browna w H=1/2

Teoria prawdopodobieństwa i modelowanie stochastyczne
Osoba referująca: 
Tomasz Rolski (Uniwersytet Wrocławski)
czwartek, 19. Maj 2022 - 12:15
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