Geodesic
Lacunary Fractional brownian Motion
ESAIM: Probability and Statistics, Tome 16 (2012), pp. 352-374

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In this paper, a new class of Gaussian field is introduced called Lacunary Fractional Brownian Motion. Surprisingly we show that usually their tangent fields are not unique at every point. We also investigate the smoothness of the sample paths of Lacunary Fractional Brownian Motion using wavelet analysis.

DOI : 10.1051/ps/2010014
Classification : 42C40, 26B35
Keywords: lacunary gaussian fields, non uniqueness of the tangent field, uniform irregularity, wavelets 
Clausel, Marianne. Lacunary Fractional brownian Motion. ESAIM: Probability and Statistics, Tome 16 (2012), pp. 352-374. doi: 10.1051/ps/2010014
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     author = {Clausel, Marianne},
     title = {Lacunary {Fractional} brownian {Motion}},
     journal = {ESAIM: Probability and Statistics},
     pages = {352--374},
     year = {2012},
     publisher = {EDP-Sciences},
     volume = {16},
     doi = {10.1051/ps/2010014},
     mrnumber = {2966168},
     zbl = {1266.60072},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps/2010014/}
}
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