An explicit positivity preserving numerical scheme for CIR/CEV type delay models with jump

DOI10.1016/j.cam.2019.04.005zbMath1420.65008arXiv1803.00327OpenAlexW2964011041MaRDI QIDQ2315818

Ioannis S. Stamatiou

Publication date: 26 July 2019

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.00327

zbMATH Keywords

semi-discrete methodexplicit numerical schemestochastic delay differential equations with jumpsboundary preserving numerical algorithmjump-delay CIR and CEV modelsnon-linear SDEs

Mathematics Subject Classification ID

Probabilistic models, generic numerical methods in probability and statistics (65C20) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stability and convergence of numerical methods for ordinary differential equations (65L20) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)

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A note on the asymptotic stability of the semi-discrete method for stochastic differential equations ⋮ Strong convergence of the split-step backward Euler method for stochastic delay differential equations with a nonlinear diffusion coefficient ⋮ Tamed EM schemes for neutral stochastic differential delay equations with superlinear diffusion coefficients ⋮ Harnack and super poincaré inequalities for generalized Cox-Ingersoll-Ross model ⋮ The semi-discrete method for the approximation of the solution of stochastic differential equations ⋮ Positivity and convergence of the balanced implicit method for the nonlinear jump-extended CIR model ⋮ On a positivity preserving numerical scheme for jump-extended CIR process: the alpha-stable case ⋮ The positive numerical solution for stochastic age-dependent capital system based on explicit-implicit algorithm ⋮ Pathwise stability and positivity of semi-discrete approximations of the solution of nonlinear stochastic differential equations

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