| Asymptotic expansions at any time for fractional scalar SDEs of Hurst index H>1/2 (2007) | |||||||||||||
Abstract | |||||||||||||
| We study the asymptotic developments with respect to $h$ of E[D_h f(X_t)], E[D_h f(X_t)|F_t] and E[D_h f(X_t)|X_t], where D_h f(X_t)=f(X_{t+h})-f(X_t), when f:R->R is a smooth real function, t is a fixed time, X is the solution of a one-dimensional stochastic differential equation driven by a fractional Brownian motion of Hurst index H>1/2 and F is its natural filtration. | |||||||||||||
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