Numerical methods for simulation of stochastic differential equations

被引：45
|
作者：
Bayram, Mustafa [1 ]
Partal, Tugcem [2 ]
Buyukoz, Gulsen Orucova [3 ]
机构：
[1] Istanbul Gelisim Univ, Dept Comp Engn, TR-34315 Istanbul, Turkey
[2] Yildiz Tech Univ, Dept Math Engn, TR-34210 Istanbul, Turkey
[3] Yildiz Tech Univ, Dept Math, TR-34210 Istanbul, Turkey
来源：
ADVANCES IN DIFFERENCE EQUATIONS | 2018年
关键词：
stochastic differential equations; Monte Carlo methods; Euler-Maruyama method; Milstein method;
D O I：
10.1186/s13662-018-1466-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we are concerned with numerical methods to solve stochastic differential equations (SDEs), namely the Euler-Maruyama (EM) and Milstein methods. These methods are based on the truncated Ito-Taylor expansion. In our study we deal with a nonlinear SDE. We approximate to numerical solution using Monte Carlo simulation for each method. Also exact solution is obtained from Ito's formula. To show the effectiveness of the numerical methods, approximation solutions are compared with exact solution for different sample paths. And finally the results of numerical experiments are supported with graphs and error tables.
引用
下载
收藏
页数：10
相关论文
共 50 条
  • [1] Numerical methods for simulation of stochastic differential equations
    Mustafa Bayram
    Tugcem Partal
    Gulsen Orucova Buyukoz
    Advances in Difference Equations, 2018
  • [2] Numerical methods for stochastic differential equations
    Newton, NJ
    ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 1996, 76 : 211 - 214
  • [3] Numerical methods for stochastic differential equations
    Wilkie, Joshua
    Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 2004, 70 (1 2): : 017701 - 1
  • [4] Numerical methods for stochastic differential equations
    Z Angew Math Mech ZAMM, Suppl 3 (211):
  • [5] Numerical methods for stochastic differential equations
    Wilkie, J
    PHYSICAL REVIEW E, 2004, 70 (01):
  • [6] Comment on "Numerical methods for stochastic differential equations"
    Burrage, Kevin
    Burrage, Pamela
    Higham, Desmond J.
    Kloeden, Peter E.
    Platen, Eckhard
    PHYSICAL REVIEW E, 2006, 74 (06):
  • [7] Numerical Picard Iteration Methods for Simulation of Non-Lipschitz Stochastic Differential Equations
    Geiser, Juergen
    SYMMETRY-BASEL, 2020, 12 (03):
  • [8] An algorithmic introduction to numerical simulation of stochastic differential equations
    Higham, DJ
    SIAM REVIEW, 2001, 43 (03) : 525 - 546
  • [9] New general methods for numerical stochastic differential equations
    Gregory, J
    Hughes, HR
    UTILITAS MATHEMATICA, 2003, 63 : 53 - 64
  • [10] Numerical methods for backward stochastic differential equations: A survey
    Chessari, Jared
    Kawai, Reiichiro
    Shinozaki, Yuji
    Yamada, Toshihiro
    PROBABILITY SURVEYS, 2023, 20 : 486 - 567
12345