TY - JOUR
T1 - Mixed fractional Brownian motion
T2 - A spectral take
AU - Chigansky, P.
AU - Kleptsyna, M.
AU - Marushkevych, D.
N1 - Publisher Copyright:
© 2019 Elsevier Inc.
PY - 2020/2/15
Y1 - 2020/2/15
N2 - This paper provides yet another look at the mixed fractional Brownian motion (fBm), this time, from the spectral perspective. The main result is an asymptotic approximation for the eigenvalues of its covariance operator. Using this approximation we derive the exact asymptotics of the L2-small ball probabilities, which was previously known only with logarithmic accuracy. The obtained expression exhibits an interesting stratification of scales, which occurs at certain values of the Hurst parameter of the fractional component. Some of them have been previously encountered in other problems involving such mixtures.
AB - This paper provides yet another look at the mixed fractional Brownian motion (fBm), this time, from the spectral perspective. The main result is an asymptotic approximation for the eigenvalues of its covariance operator. Using this approximation we derive the exact asymptotics of the L2-small ball probabilities, which was previously known only with logarithmic accuracy. The obtained expression exhibits an interesting stratification of scales, which occurs at certain values of the Hurst parameter of the fractional component. Some of them have been previously encountered in other problems involving such mixtures.
KW - Fractional Brownian motion
KW - Gaussian processes
KW - Small ball probabilities
KW - Spectral problem
UR - http://www.scopus.com/inward/record.url?scp=85072809521&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2019.123558
DO - 10.1016/j.jmaa.2019.123558
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:85072809521
SN - 0022-247X
VL - 482
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
M1 - 123558
ER -