Survival exponents for some Gaussian processes
George Molchan
TL;DR
This paper investigates the asymptotic behavior of the probability that certain Gaussian processes, like fractional Brownian motion, stay below a fixed level over long periods, providing estimates for the associated survival exponents.
Contribution
It introduces new estimates for the survival exponents of self-similar Gaussian processes, including fractional Brownian motion and its integral, in long-time asymptotics.
Findings
Derived power-law asymptotics for Gaussian processes.
Estimated survival exponents for fractional Brownian motion.
Analyzed integrated fractional Brownian motion in large intervals.
Abstract
The problem is a power-law asymptotics of the probability that a self-similar process does not exceed a fixed level during long time. The exponent in such asymptotics is estimated for some Gaussian processes, including the fractional Brownian motion (FBM) in (-T1,T),T>T1>>1 and the integrated FBM in(0,T), T>>1 .
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Taxonomy
TopicsStochastic processes and statistical mechanics · Financial Risk and Volatility Modeling · Stochastic processes and financial applications