Existence and Uniqueness of the Solution of Stochastic Differential Equation Involving Wiener Process and Fractional Brownian Motion with Hurst IndexH > 1/2

DOI10.1080/03610926.2011.581174zbMath1315.60071arXiv1103.0615OpenAlexW1598203903MaRDI QIDQ2890082

Yuliya S. Mishura, Georgiy M. Shevchenko

Publication date: 8 June 2012

Published in: Communications in Statistics - Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1103.0615

zbMATH Keywords

fractional Brownian motionEuler approximationmixed stochastic differential equationpathwise integral

Mathematics Subject Classification ID

Gaussian processes (60G15) Fractional processes, including fractional Brownian motion (60G22) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Brownian motion (60J65)

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Cites Work

• Integration with respect to fractal functions and stochastic calculus. I
• The existence and uniqueness of the solution of an integral equation driven by a \(p\)-semimartin\-gale of special type.
• Monotonicity of certain functionals under rearrangement
• Stochastic calculus for fractional Brownian motion and related processes.
• Stochastic Differential Equations Driven by Fractional Brownian Motion and Standard Brownian Motion
• Stieltjes integrals of Hölder continuous functions with applications to fractional Brownian motion

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