Bifractional Brownian motion: existence and border cases

Lifshits, Mikhail; Volkova, Ksenia

doi:10.1051/ps/2015015

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Bifractional Brownian motion: existence and border cases

Lifshits, Mikhail ^1,² ; Volkova, Ksenia ¹

¹ St. Petersburg State University, 28 Stary, Peterhof, Bibliotechnaya pl.,2, 198504 St. Petersburg, Russia.
² MAI, Linköping University, 58183 Linköping, Sweden.

ESAIM: Probability and Statistics, Tome 19 (2015), pp. 766-781

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Résumé

Bifractional Brownian motion (bfBm) is a centered Gaussian process with covariance $R^{(H, K)} (s, t) = 2^{- K} ({(| s |}^{2 H} + {| t |}^{2 H})^{K} - {| t - s |}^{2 HK}), s, t \in ℝ$

We study the existence of bfBm for a given pair of parameters $(H, K)$ and encounter some related limiting processes.

Zbl

DOI : 10.1051/ps/2015015

Classification : 60G15, 42A82
Keywords: Bifractional Brownian motion, Gaussian process, fractional Brownian motion

Affiliations des auteurs :

Lifshits, Mikhail ^{1, 2} ; Volkova, Ksenia ¹

¹ St. Petersburg State University, 28 Stary, Peterhof, Bibliotechnaya pl.,2, 198504 St. Petersburg, Russia.
² MAI, Linköping University, 58183 Linköping, Sweden.

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     author = {Lifshits, Mikhail and Volkova, Ksenia},
     title = {Bifractional {Brownian} motion: existence and border cases},
     journal = {ESAIM: Probability and Statistics},
     pages = {766--781},
     publisher = {EDP-Sciences},
     volume = {19},
     year = {2015},
     doi = {10.1051/ps/2015015},
     zbl = {1333.60075},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps/2015015/}
}

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Lifshits, Mikhail; Volkova, Ksenia. Bifractional Brownian motion: existence and border cases. ESAIM: Probability and Statistics, Tome 19 (2015), pp. 766-781. doi: 10.1051/ps/2015015

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