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In this article, we study the numerical approximation of stochastic differential equations driven by a multidimensional fractional Brownian motion (fBm) with Hurst parameter greater than 1/3. We introduce an implementable scheme for these equations, which is based on a second-order Taylor expansion, where the usual Lévy area terms are replaced by products of increments of the driving fBm. The convergence of our scheme is shown by means of a combination of rough paths techniques and error bounds...
In this article, we consider an -dimensional stochastic differential equation driven by a fractional brownian motion with Hurst parameter >1/3. We derive an expansion for [(
)] in terms of , where denotes the solution to the SDE and :ℝ→ℝ is a regular function. Comparing to F. Baudoin and L. Coutin,
(2007) 550–574, where the same problem is studied, we provide an improvement in three different directions: we are able to consider equations with drift, we parametrize...
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