Geodesic
On differentiability of solution to
Teoriâ slučajnyh processov, Tome 13 (2007) no. 2, pp. 243-250

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Stochastic differential equation with pathwise integral with respect to fractional Brownian motion is considered. For solution of such equation, under different conditions, the Malliavin differentiability is proved. Under infinite differentiability and boundedness of derivatives of the coefficients it is proved that the solution is infinitely differentiable in the Malliavin sense with all derivatives bounded.
Keywords: Fractional Brownian motion, pathwise integral, stochastic differential equation, Malliavin derivative. 
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     author = {Yu. S. Mishura and G. M. Shevchenko},
     title = {On differentiability of solution to},
     journal = {Teori\^a slu\v{c}ajnyh processov},
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     publisher = {mathdoc},
     volume = {13},
     number = {2},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2007_13_2_a7/}
}
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Yu. S. Mishura; G. M. Shevchenko. On differentiability of solution to. Teoriâ slučajnyh processov, Tome 13 (2007) no. 2, pp. 243-250. http://geodesic.mathdoc.fr/item/THSP_2007_13_2_a7/