Geodesic
Linear problems for a fractional Brownian motion: Group approach
Teoriâ veroâtnostej i ee primeneniâ, Tome 47 (2002) no. 1, pp. 59-70

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For the fractional Brownian motion (fBm) the problem of extrapolation from a segment, the canonical representation of fBm via white noise on a segment and their reciprocal relation, and Girsanov's formula are considered. A general approach to these problems is based on the invariance of fBm with respect to linear rational transformations of time. This approach practically excludes the solution of integral equations and explains the efficiency of the aforementioned problems for fBm.
Keywords: fractional Brownian motion, Girsanov's formula.
Mots-clés : extrapolation 
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     author = {G. M. Molchan},
     title = {Linear problems for a fractional {Brownian} motion: {Group} approach},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {59--70},
     publisher = {mathdoc},
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     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2002_47_1_a3/}
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G. M. Molchan. Linear problems for a fractional Brownian motion: Group approach. Teoriâ veroâtnostej i ee primeneniâ, Tome 47 (2002) no. 1, pp. 59-70. http://geodesic.mathdoc.fr/item/TVP_2002_47_1_a3/