Fractional Brownian Motion: Small Increments and First Exit Time from One-sided Barrier (Qidi Peng, CGU)

Abstract: The talk introduces a conjecture on the first exit time of fractional Brownian motion: the upper-tail probability for a fractional Brownian motion to first exit a positive-valued barrier over time T has the exact asymptotic rate T^(H-1), where H is the Hurst parameter of the fractional Brownian motion. The talk tries to understand this conjecture by providing several equivalent statements. We then introduce the best effort made in the current literature towards solving this conjecture.