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.
Keywords: lacunary gaussian fields, non uniqueness of the tangent field, uniform irregularity, wavelets
@article{PS_2012__16__352_0, author = {Clausel, Marianne}, title = {Lacunary {Fractional} brownian {Motion}}, journal = {ESAIM: Probability and Statistics}, pages = {352--374}, publisher = {EDP-Sciences}, volume = {16}, year = {2012}, doi = {10.1051/ps/2010014}, mrnumber = {2966168}, zbl = {1266.60072}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/ps/2010014/} }
Clausel, Marianne. Lacunary Fractional brownian Motion. ESAIM: Probability and Statistics, Volume 16 (2012), pp. 352-374. doi : 10.1051/ps/2010014. http://archive.numdam.org/articles/10.1051/ps/2010014/
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