Asymptotic distribution of the derivative of the taut string accompanying Wiener process
Abstract
In the article, we find the asymptotic distribution of the derivative of the taut string accompanying a Wiener process W in a strip of fixed width on long time intervals. This enables to find explicit expressions for the limits limT→∞ 1 Tinf∫0Tφ(h′(t))dt, where infimum is taken over the class of functions h satisfying assumptions h∈AC[0,T],h(0)=(0),h(T)=W(T),maxt∈[0,T]|h(t)−W(t)|≤r 2. For example, for kinetic energy φ(u)=u2 which was considered earlier by Lifshits and Setterqvist [5], the limiting value equals to π26r2.
Fields of Study & Subjects
Stochastic processes and statistical mechanics
Stochastic processes and financial applications
Probability and Statistical Research
Publication details
- Journal / source
- Electronic Journal of Probability
- Volume
- 31
- Issue
- none
- Pages
- 1–20
- Publication date
- 1 January 2026
- Language
- EN