数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (3): 747-763.doi: 10.1007/s10473-019-0308-1

• 论文 • 上一篇    下一篇

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
  • 收稿日期:2018-03-31 修回日期:2018-08-23 出版日期:2019-06-25 发布日期:2019-06-27
  • 通讯作者: Samy TINDEL E-mail:stindel@purdue.edu
  • 作者简介:Johanna GARZÓN,E-mail:mjgarzonm@unal.edu.co;Soledad TORRES,E-mail:soledad.torres@uv.cl
  • 基金资助:
    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).

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).

摘要: 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.

关键词: Fractional Brownian motion, stochastic differential equations, rough paths, discrete time approximation

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

中图分类号: 

  • 60H15