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Convergence of stochastic differential equations driven by fractional Brownian motions. (Chinese. English summary) Zbl 1413.34203
Summary: A class of stochastic differential equations driven by fractional Brownian motions is considered. We derive that the sequential solutions almost sure and \({\mathcal{L}^p}\) converge to the solution of the limit equation. Furthermore, we show that the difference between Euler approximation of sequential equations and limit equation converges almost surely to a random variable, which in particular depends on the Malliavin derivative of the solution of the limit equation.
MSC:
34F05 Ordinary differential equations and systems with randomness
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60G22 Fractional processes, including fractional Brownian motion
34D05 Asymptotic properties of solutions to ordinary differential equations
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