stochastic

A MAPLE package for stochastic differential equations. The author has developed a MAPLE package containing routines which return explicit solutions of those stochastic differential equations (SDEs) dx t =a(t,x t )dt+b(t,x t )dw t. known to have such solutions, and routines which construct efficient, high-order stochastic numerical schemes. The MAPLE package, which is called ‘stochastic’, was created to fulfil a need for commands able to solve SDEs both explicitly and numerically. There had previously been no such commands in MAPLE as SDEs do not conform to the rules of deterministic calculus. The construction of higher-order schemes by hand would be a very complex and laborious task as a consequence of the repeated application of the operators L 0 =∂ ∂t+a(t,x)∂ ∂x+1 2b(t,x) 2 ∂ 2 ∂x 2 ,L 1 =b(t,x)∂ ∂x· .This paper includes stochastic numerical schemes and demonstrates procedures from the stochastic package which automate the construction of such schemes.


References in zbMATH (referenced in 16 articles , 2 standard articles )

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  1. Kuznetsov, Mikhail Dmitrievich; Kuznetsov, Dmitriy Feliksovich: SDE-MATH: a software package for the implementation of strong high-order numerical methods for Ito SDEs with multidimensional non-commutative noise based on multiple Fourier-Legendre series (2021)
  2. Mummert, Anna; Otunuga, Olusegun M.: Parameter identification for a stochastic \textitSEIRSepidemic model: case study influenza (2019)
  3. Ansmann, Gerrit: Efficiently and easily integrating differential equations with JiTCODE, JiTCDDE, and JiTCSDE (2018)
  4. Merdan, Mehmet; Bekiryazici, Zafer; Kesemen, Tulay; Khaniyev, Tahir: Comparison of stochastic and random models for bacterial resistance (2017)
  5. Amano, Kazuo: Newton-Milstein scheme for stochastic differential equations and its fast uniform convergence (2016)
  6. Sun, Yifei; Kumar, Mrinal: A numerical solver for high dimensional transient Fokker-Planck equation in modeling polymeric fluids (2015)
  7. Josa-Fombellida, Ricardo; Rincón-Zapatero, Juan Pablo: Stochastic pension funding when the benefit and the risky asset follow jump diffusion processes (2012)
  8. Aït-Sahalia, Yacine: Closed-form likelihood expansions for multivariate diffusions (2008)
  9. Gilsing, Hagen; Shardlow, Tony: SDELab: A package for solving stochastic differential equations in MATLAB (2007)
  10. Kloeden, Peter E.; Rößler, Andreas: Runge-Kutta methods for affinely controlled nonlinear systems (2007)
  11. Grüne, L.; Kloeden, P. E.: Higher order numerical approximation of switching systems (2006)
  12. Higham, Desmond J.; Kloeden, Peter. E.: Numerical methods for nonlinear stochastic differential equations with jumps (2005)
  13. Cyganowski, Sasha; Kloeden, Peter; Ombach, Jerzy: From elementary probability to stochastic differential equations with MAPLE (2002)
  14. Cyganowski, Sasha; Kloeden, Peter; Ombach, Jerzy: From elementary probability to stochastic differential equations with MAPLE (2002) MathEduc
  15. Cyganowski, S.; Grüne, L.; Kloeden, P. E.: Maple for stochastic differential equations (2001)
  16. Cyganowski, S.: A MAPLE package for stochastic differential equations (1996)