Rate of convergence of Euler approximations of solution to mixed stochastic differential equation involving Brownian motion and fractional Brownian motion

DOI10.1515/ROSE.2011.021zbMath1290.60069arXiv1111.1845OpenAlexW3106393920WikidataQ115235790 ScholiaQ115235790MaRDI QIDQ4923228

Yuliya S. Mishura, Georgiy M. Shevchenko

Publication date: 6 June 2013

Published in: Random Operators and Stochastic Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1111.1845

zbMATH Keywords

fractional Brownian motionEuler approximationmixed stochastic differential equationpathwise integral

Mathematics Subject Classification ID

Fractional processes, including fractional Brownian motion (60G22) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Brownian motion (60J65) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35)

Related Items (7)

Regularization of differential equations by two fractional noises ⋮ Rate of convergence of Euler approximation of time-dependent mixed SDEs driven by Brownian motions and fractional Brownian motions ⋮ Convergence of solutions of mixed stochastic delay differential equations with applications ⋮ Mixed stochastic differential equations with long-range dependence: existence, uniqueness and convergence of solutions ⋮ On mixed fractional stochastic differential equations with discontinuous drift coefficient ⋮ Parameter estimation in mixed fractional stochastic heat equation ⋮ Weak convergence of SFDEs driven by fractional Brownian motion with irregular coefficients

Cites Work

• Mixed fractional Brownian motion
• The existence and uniqueness of the solution of an integral equation driven by a \(p\)-semimartin\-gale of special type.
• Exact rate of convergence of some approximation schemes associated to SDEs driven by a fractional Brownian motion
• Existence and Uniqueness of the Solution of Stochastic Differential Equation Involving Wiener Process and Fractional Brownian Motion with Hurst IndexH > 1/2
• Stochastic Differential Equations Driven by Fractional Brownian Motion and Standard Brownian Motion

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