Asymptotics of Karhunen-Loève Eigenvalues for sub-fractional Brownian motion and its application

2021/10/07 by Jun-Qi Hu, Yingli Wang, Hu, Jun-Qi +3
Economics, Econometrics and Finance · #47B40 #60G15 #60G22 #Complex Systems and Time Series Analysis #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Spectral Theory (math.SP) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2110.03203

openalex publication_date 2021/10/07 · openalex created_date 2021/10/11 · openalex updated_date 2026/07/28

Abstract

In the present paper, the Karhunen-Loève eigenvalues for a sub-fractional Brownian motion are considered in the case of H>\frac12. Rigorous large n asymptotics for those eigenvalues are shown, based on functional analysis method. By virtue of these asymptotics, along with some standard large deviations results, asymptotically estimates for the closely related problem of small L²-ball probabilities for a sub-fractional Brownian motion are derived. By the way, asymptotic analysis on the Karhunen-Loève eigenvalues for the corresponding "derivative" process is also established.

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