Numerical Scheme for Stochastic Differential Equations Driven by Fractional Brownian Motion with 1/4<H<1/2

Numerical Scheme for Stochastic Differential Equations Driven by Fractional Brownian Motion with 1/4<H<1/2

In this article, we study a numerical scheme for stochastic differential equations driven by fractional Brownian motion with Hurst parameter H ∈ 1 / 4 , 1 / 2 . Toward this end, we apply Doss–Sussmann representation of the solution and an approximation of this representation using a first-order Tayl...

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Veröffentlicht in:Journal of theoretical probability 2020-09, Vol.33 (3), p.1211-1237
Hauptverfasser: Araya, Héctor, León, Jorge A., Torres, Soledad
Format: Artikel
Sprache:eng
Schlagworte:
Brownian motion
Differential equations
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Representations
Statistics
Taylor series
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Zusammenfassung:In this article, we study a numerical scheme for stochastic differential equations driven by fractional Brownian motion with Hurst parameter H ∈ 1 / 4 , 1 / 2 . Toward this end, we apply Doss–Sussmann representation of the solution and an approximation of this representation using a first-order Taylor expansion. The obtained rate of convergence is n - 2 H + ρ , for ρ small enough.
ISSN:0894-9840
1572-9230
DOI:10.1007/s10959-019-00902-3