Construction of positivity preserving numerical schemes for some multidimensional stochastic differential equations

DOI10.3934/DCDSB.2015.20.153zbMath1325.65017arXiv1310.1581OpenAlexW2964041394MaRDI QIDQ480036

Nikolaos Halidias

Publication date: 8 December 2014

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1310.1581

zbMATH Keywords

positivity preservingexplicit numerical schememultidimensional super linear stochastic differential equationsstochastic predator-prey model

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)

Related Items (9)

A note on the asymptotic stability of the semi-discrete method for stochastic differential equations ⋮ On the construction of boundary preserving numerical schemes ⋮ Stability analysis of stochastic delay differential equations with Markovian switching driven by Lévy noise ⋮ A boundary preserving numerical scheme for the Wright-Fisher model ⋮ Construction of positivity preserving numerical method for stochastic age-dependent population equations ⋮ An explicit and positivity preserving numerical scheme for the mean reverting CEV model ⋮ The semi-discrete method for the approximation of the solution of stochastic differential equations ⋮ The positive numerical solution for stochastic age-dependent capital system based on explicit-implicit algorithm ⋮ Positivity-preserving numerical schemes for stochastic differential equations

Cites Work

• Convergence, nonnegativity and stability of a new Milstein scheme with applications to finance
• Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients
• First order strong approximations of scalar SDEs defined in a domain
• Strong convergence of the stopped Euler-Maruyama method for nonlinear stochastic differential equations
• A novel approach to construct numerical methods for stochastic differential equations
• Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients
• Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations

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