Transformation formulas for fractional Brownian motion |
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Authors: | Cé line Jost |
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Affiliation: | Department of Mathematics and Statistics, P.O. Box 68 (Gustaf Hällströmin katu 2b), 00014 University of Helsinki, Finland |
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Abstract: | We derive a Molchan–Golosov-type integral transform which changes fractional Brownian motion of arbitrary Hurst index K into fractional Brownian motion of index H. Integration is carried out over [0,t], t>0. The formula is derived in the time domain. Based on this transform, we construct a prelimit which converges in L2(P)-sense to an analogous, already known Mandelbrot–Van Ness-type integral transform, where integration is over (−∞,t], t>0. |
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Keywords: | 60G15 60G18 26A33 60H05 |
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