The rate of convergence for Euler approximations of solutions of stochastic differential equations driven by fractional Brownian motion

By Yuliya S. Mishura, Georgiy Shevchenko. 2007

86 citations recorded by the source corpus.

The paper focuses on discrete-type approximations of solutions to non-homogeneous stochastic differential equations (SDEs) involving fractional Brownian motion (fBm). We prove that the rate of convergence for Euler approximations of solutions of pathwise SDEs driven by fBm with Hurst index H>1/2 can be estimated by , where δ is the diameter of partition used for discretization. For discrete-time approximations of Skorohod-type quasilinear equation driven by fBm we prove that the rate of convergence is .

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/f7cc8469371a2b792c7ab28aabc1f46e3a1d2251

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Citations in the corpus

• A Milstein-type scheme without Lévy area terms for SDEs driven by fractional Brownian motion (2010, background): “in [26], where an almost sure convergence rate n with ε > 0 arbitrarily small is established.”
• Controlled differential equations as Young integrals: A simple approach (2010, background): “Keywords: controlled differential equations, Young integral, fractional Brownian motion, rough paths, flow property, Euler scheme.”