Numerical Analysis of Stochastic Differential Equations with Explosions

DOI10.1081/SAP-200064484zbMath1080.65004OpenAlexW1999567026MaRDI QIDQ5312735

Julio D. Rossi, Mariela Sued, Juan Dávila, Julián Fernández Bonder, Pablo Groisman

Publication date: 25 August 2005

Published in: Stochastic Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1081/sap-200064484

zbMATH Keywords

numerical examplesstochastic differential equationsinitial value problemsadaptive methodsstepsize controlblow upsEuler-Maruyama methodexplosion time

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) Generation, random and stochastic difference and differential equations (37H10) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items (9)

Numerical and mathematical analysis of blow-up problems for a stochastic differential equation ⋮ Preservation of the growth rates of delay differential equations by Euler schemes with non-uniform step sizes ⋮ Uniqueness and explosion time of solutions of stochastic differential equations driven by fractional Brownian motion ⋮ An Osgood criterion for integral equations with applications to stochastic differential equations with an additive noise ⋮ Some Feller and Osgood type criteria for semilinear stochastic differential equations ⋮ Almost sure stability of the Euler-Maruyama method with random variable stepsize for stochastic differential equations ⋮ Distribution function of the blow up time of the solution of an anticipating random fatigue equation ⋮ Time-space white noise eliminates global solutions in reaction-diffusion equations ⋮ Positivity-preserving numerical schemes for stochastic differential equations

Cites Work

• An adaptive time step procedure for a parabolic problem with blow-up
• An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations
• Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations

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