On the passage times of self-similar Gaussian processes on curved boundaries
Abstract
Let $T_{c,β}$ denote the smallest $t\ge1$ that a continuous, self-similar Gaussian process with self-similarity index $α>0$ moves at least $\pm c t^β$ units. We prove that: (i) If $β>α$, then $T_{c,β}=\infty$ with positive probability; (ii) If $β
Fields of Study & Subjects
Stochastic processes and financial applications
Stochastic processes and statistical mechanics
Fractional Differential Equations Solutions
Publication details
- Journal / source
- Bernoulli
- Volume
- 32
- Issue
- 3
- Publication date
- 29 April 2026
- Language
- EN