Articles

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

  • Johanna GARZÓN ,
  • Samy TINDEL ,
  • Soledad TORRES
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  • 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 date: 2018-03-31

  Revised date: 2018-08-23

  Online published: 2019-06-27

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.

Cite this article

Johanna GARZÓN , Samy TINDEL , Soledad TORRES . EULER SCHEME FOR FRACTIONAL DELAY STOCHASTIC DIFFERENTIAL EQUATIONS BY ROUGH PATHS TECHNIQUES[J]. Acta mathematica scientia, Series B, 2019 , 39(3) : 747 -763 . DOI: 10.1007/s10473-019-0308-1

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