A Stability Result for Stochastic Differential Equations Driven by Fractional Brownian Motions | Zendy

Bruno Saussereau | Zendy

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A Stability Result for Stochastic Differential Equations Driven by Fractional Brownian Motions

Author(s) -

Bruno Saussereau

Publication year - 2012

Publication title -

international journal of stochastic analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.19

H-Index - 28

eISSN - 2090-3340

pISSN - 2090-3332

DOI - 10.1155/2012/281474

Subject(s) - mathematics , fractional brownian motion , stochastic differential equation , brownian noise , brownian motion , mathematical analysis , diffusion process , hurst exponent , limit (mathematics) , stability (learning theory) , sequence (biology) , stochastic partial differential equation , geometric brownian motion , differential equation , innovation diffusion , statistics , knowledge management , white noise , machine learning , biology , computer science , genetics

We study the stability of the solutions of stochastic differential equations driven by fractional Brownian motions with Hurst parameter greater than half. We prove that when the initial conditions, the drift, and the diffusion coefficients as well as the fractional Brownian motions converge in a suitable sense, then the sequence of the solutions of the corresponding equations converge in Hölder norm to the solution of a stochastic differential equation. The limit equation is driven by the limit fractional Brownian motion and its coefficients are the limits of the sequence of the coefficients

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