Taylor schemes for rough differential equations and fractional diffusions

DOI10.3934/dcdsb.2016090zbMath1353.60064arXiv1510.08732OpenAlexW2963056784MaRDI QIDQ727475

Yaozhong Hu, David Nualart, Yanghui Liu

Publication date: 7 December 2016

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.08732

zbMATH Keywords

fractional Brownian motionstochastic differential equationsnumerical approximationalmost sure convergence ratemultiple integralsrough differential equations\(L^p\)-convergence rategeneralized Leibniz ruleTaylor schemes

Mathematics Subject Classification ID

Fractional processes, including fractional Brownian motion (60G22) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Strong limit theorems (60F15) Stability and convergence of numerical methods for ordinary differential equations (65L20) Stochastic integrals (60H05) Stochastic calculus of variations and the Malliavin calculus (60H07) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30) (L^p)-limit theorems (60F25)

Related Items (4)

Convergence of trapezoid rule to rough integrals ⋮ First-order Euler scheme for SDEs driven by fractional Brownian motions: the rough case ⋮ Crank-Nicolson scheme for stochastic differential equations driven by fractional Brownian motions ⋮ Symplectic Runge-Kutta methods for Hamiltonian systems driven by Gaussian rough paths

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