Geodesic
Local time as an element of the Sobolev space
Teoriâ slučajnyh processov, Tome 13 (2007) no. 3, pp. 65-79

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For a centered Gaussian random field taking its values in d, we investigate the existence of a local time as a generalized functional, i.e an element of some Sobolev space. We give the sufficient condition for such an existence in terms of the field covariation and apply it in several examples: the self-intersection local time for a fractional Brownian motion and the intersection local time for two Brownian motions.
Keywords: Local time, Itô–Wiener expansion, Gaussian random field, fractional Brownian motion.
Mots-clés : Sobolev spaces 
@article{THSP_2007_13_3_a7,
     author = {Alexey V. Rudenko},
     title = {Local time as an element of the {Sobolev} space},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {65--79},
     publisher = {mathdoc},
     volume = {13},
     number = {3},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2007_13_3_a7/}
}
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Alexey V. Rudenko. Local time as an element of the Sobolev space. Teoriâ slučajnyh processov, Tome 13 (2007) no. 3, pp. 65-79. http://geodesic.mathdoc.fr/item/THSP_2007_13_3_a7/