On local linearization method for stochastic differential equations driven by fractional Brownian motion. Issue 1 (2nd January 2021)

• Record Type: Journal Article
• Authors: Araya, Héctor; León, Jorge A.; Torres, Soledad
• Is Part Of: Stochastic analysis and applications. Volume 39:Issue 1(2021)
• Page Start: 55
• Page End: 90
• Publication Date: 2021-01-02
• Subjects: Fractional Brownian motion -- local linearization -- stochastic differential equation -- Taylor theorem -- Young integral; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2020.1779746
• Languages: English
• ISSNs: 0736-2994

Abstract

Abstract: We propose a local linearization scheme to approximate the solutions of non-autonomous stochastic differential equations driven by fractional Brownian motion with Hurst parameter 1 / 2 < H < 1 . Toward this end, we approximate the drift and diffusion terms by means of a first-order Taylor expansion. This becomes the original equation into a local fractional linear stochastic differential equation, whose solution can be figured out explicitly. As in the Brownian motion case (i.e., H = 1/2), the rate of convergence, in our case, is twice the one of the Euler scheme. Numerical examples are given to demonstrate the performance of the method.