Taylor expansion for the solution of a stochastic differential equation driven by fractional Brownian motions

2011/12/13 by Baudoin, Fabrice, Zhang, Xuejing
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1112.2760

Abstract

We study the Taylor expansion for the solution of a differential equation driven by a multidimensional Holder path with exponent β> 1/2. We derive a convergence criterion that enables us to write the solution as an infinite sum of iterated integrals on a nonempty interval. We apply our deterministic results to stochastic differential equations driven by fractional Brownian motions with Hurst parameter H > 1\2. We also prove that by using L₂ estimates of iterated integrals, the criterion and the speed of convergence for the stochastic Taylor expansion can be improved using Borel-Cantelli type arguments when H∈ (1/2, 3/4).

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