Stochastic Differential Equations Driven by Fractional Brownian Motion and Standard Brownian Motion |
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| Authors: | João Guerra David Nualart |
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| Institution: | 1. Department of Mathematics , ISEG–Technical University of Lisbon and CEMAPRE , Lisbon, Portugal jguerra@iseg.utl.pt;3. Department of Mathematics , University of Kansas , Lawrence, Kansas, USA |
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| Abstract: | Abstract We prove an existence and uniqueness theorem for solutions of multidimensional, time dependent, stochastic differential equations driven simultaneously by a multidimensional fractional Brownian motion with Hurst parameter H > 1/2 and a multidimensional standard Brownian motion. The proof relies on some a priori estimates, which are obtained using the methods of fractional integration and the classical Itô stochastic calculus. The existence result is based on the Yamada–Watanabe theorem. |
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| Keywords: | Fractional Brownian motion Stochastic differential equations |
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