Taylor expansion for the solution of a stochastic differential equation driven by fractional Brownian motions
نویسندگان
چکیده
We study the Taylor expansion for the solution of a differential equation driven by a multi-dimensional Hölder 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 study the convergence in L of the stochastic Taylor expansion by using L estimates of iterated integrals and Borel-Cantelli type arguments.
منابع مشابه
Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion
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