Persistence probabilities of a smooth self-similar anomalous diffusion process

2023/11/07 by Frank Aurzada, Aurzada, Frank, Pascal Mittenbühler +1
Biochemistry, Genetics and Molecular Biology · Economics, Econometrics and Finance · Mathematics · #60G15 #60G22 #Complex Systems and Time Series Analysis #Diffusion and Search Dynamics #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2311.03972

openalex publication_date 2023/11/07 · openalex created_date 2023/11/09 · openalex updated_date 2026/07/28

Abstract

We consider the persistence probability of a certain fractional Gaussian process M^H that appears in the Mandelbrot-van Ness representation of fractional Brownian motion. This process is self-similar and smooth. We show that the persistence exponent of M^H exists and is continuous in the Hurst parameter H. Further, the asymptotic behaviour of the persistence exponent for H\downarrow0 and H\uparrow1, respectively, is studied. Finally, for H→ 1/2, the suitably renormalized process converges to a non-trivial limit with non-vanishing persistence exponent, contrary to the fact that M^1/2 vanishes.

Related

• Universality for persistence exponents of local times of self-similar processes with stationary increments
• Persistence exponent for random processes in Brownian scenery
• Persistence probabilities for fractionally integrated fractional Brownian noise
• Survival exponents for some Gaussian processes
• Persistence probabilities of spherical fractional Brownian motion