Second order limit laws for occupation times of the fractional Brownian motion
Fangjun Xu
TL;DR
This paper establishes second order limit laws for additive functionals of multi-dimensional fractional Brownian motion with Hurst index 1/d, extending classical results using the method of moments.
Contribution
It introduces new second order limit laws for occupation times of fractional Brownian motion at the critical Hurst index, extending the Kallianpur-Robbins law.
Findings
Proves second order limit laws for fractional Brownian motion occupation times.
Extends classical laws to the critical Hurst index case.
Uses the method of moments for the proofs.
Abstract
We prove second order limit laws for (additive) functionals of the -dimensional fractional Brownian motion with Hurst index , using the method of moments, extending the Kallianpur-Robbins law.
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Taxonomy
TopicsStochastic processes and financial applications · Financial Risk and Volatility Modeling · Stochastic processes and statistical mechanics