On differentiability of solution to stochastic differential equation with fractional brownian motion

Yu. S. Mishura, G. M. Shevchenko

Department of Probability Theory and Mathematical Statistics, Kyiv National Taras Shevchenko University, Kyiv, Ukraine

Abstract: 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.

MSC: Primary 60H05; Secondary 60H07

Language: English

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