Stability of weak numerical schemes for stochastic differential equations

DOI10.1016/0898-1221(94)00185-5zbMath0810.65147OpenAlexW1998530334MaRDI QIDQ5906613

Norbert Hofmann, Eckhard Platen

Publication date: 9 April 1995

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0898-1221(94)00185-5

zbMATH Keywords

absolute stabilityWiener processstochastic differential equationsnumerical stabilitymultiplicative noiseimplicit Euler schemestability regionsexplicit Euler schemeStratonovich type test equations

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stability and convergence of numerical methods for ordinary differential equations (65L20) Ordinary differential equations and systems with randomness (34F05) Numerical methods for initial value problems involving ordinary differential equations (65L05) Probabilistic methods, stochastic differential equations (65C99)

Related Items (13)

On weak implicit and predictor-corrector methods ⋮ Convergence and stability of the split-step \(\theta \)-method for stochastic differential equations ⋮ Stability analysis of second-order weak schemes for multi-dimensional stochastic differential systems ⋮ Mean square stability of second-order weak numerical methods for stochastic differential equations. ⋮ Method for simulating non-linear stochastic differential equations in ℝ¹ ⋮ STRONG PREDICTOR–CORRECTOR EULER METHODS FOR STOCHASTIC DIFFERENTIAL EQUATIONS ⋮ Rooted tree analysis of the order conditions of row-type scheme for stochastic differential equations ⋮ On the stability of some second order numerical methods for weak approximation of Itô SDEs ⋮ A family of Chaplygin-type solvers for Itô stochastic differential equations ⋮ Mean-square stability of second-order Runge-Kutta methods for stochastic differential equations ⋮ On the numerical stability of simulation methods for SDEs under multiplicative noise in finance ⋮ Stability of weak numerical schemes for stochastic differential equations ⋮ Diagonally drift-implicit Runge-Kutta methods of weak order one and two for Itô SDEs and stability analysis

Uses Software

• RODAS

Cites Work

• Higher-order implicit strong numerical schemes for stochastic differential equations
• Numerical Integration of Multiplicative-Noise Stochastic Differential Equations
• Option Pricing Under Incompleteness and Stochastic Volatility
• A special stability problem for linear multistep methods
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