Acta mathematica scientia,Series B ›› 2019, Vol. 39 ›› Issue (3): 747-763.doi: 10.1007/s10473-019-0308-1

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EULER SCHEME FOR FRACTIONAL DELAY STOCHASTIC DIFFERENTIAL EQUATIONS BY ROUGH PATHS TECHNIQUES

Johanna GARZÓN1, Samy TINDEL2, Soledad TORRES3   

  1. 1. Departamento de Matemáticas, Universidad Nacional de Colombia, Bogotá D. C., Colombia;
    2. Department of Mathematics, Purdue University, 150 N. University Street, W. Lafayette, IN 47907, USA;
    3. Facultad de Ingeniería, CIMFAV Universidad de Valparaíso, Casilla 123-V, 4059 Valparaiso, Chile
  • Received:2018-03-31 Revised:2018-08-23 Online:2019-06-25 Published:2019-06-27
  • Contact: Samy TINDEL E-mail:stindel@purdue.edu
  • Supported by:
    The first author is supported by MATH-AmSud 18-MATH-07 SaSMoTiDep Project and HERMES project 41305. S. Torres is partially supported by the Project ECOS-CONICYT C15E05, REDES 150038, MATH-AmSud 18-MATH-07 SaSMoTiDep Project and Fondecyt (1171335). S. Tindel is supported by NSF (Grant DMS-1613163).

Abstract: In this note, we study a discrete time approximation for the solution of a class of delayed stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H∈ (1/2, 1). In order to prove convergence, we use rough paths techniques. Theoretical bounds are established and numerical simulations are displayed.

Key words: Fractional Brownian motion, stochastic differential equations, rough paths, discrete time approximation

CLC Number: 

  • 60H15
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