Approximation of Euler-Maruyama for one-dimensional stochastic differential equations involving the maximum process

DOI10.1515/MCMA-2020-2057zbMath1434.60169OpenAlexW3006260495MaRDI QIDQ1985372

Kamal Hiderah

Publication date: 7 April 2020

Published in: Monte Carlo Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/mcma-2020-2057

zbMATH Keywords

strong convergencestochastic differential equationsmaximum processEuler-Maruyama approximation

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) Local time and additive functionals (60J55)

Cites Work

• Weak limits of perturbed random walks and the equation \(Y_ t = B_ t+\alpha\sup\{Y_ s:s \leq t\} + \beta\inf\{Y_ s:s\leq t\}\)
• A note on Euler approximations for SDEs with Hölder continuous diffusion coefficients
• On irregular functionals of SDEs and the Euler scheme
• Higher-order implicit strong numerical schemes for stochastic differential equations
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• Perturbed Brownian motions
• Some calculations for doubly perturbed Brownian motion
• Weak consistency of the Euler method for numerically solving stochastic differential equations with discontinuous coefficients
• The Euler scheme with irregular coefficients
• The law of the Euler scheme for stochastic differential equations. I: Convergence rate of the distribution function
• Upper and lower limits of doubly perturbed Brownian motion
• On the uniqueness of solutions of stochastic differential equations
• An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations
• Strong rate of convergence for the Euler-Maruyama approximation of stochastic differential equations with irregular coefficients
• Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations
• ON ONE-DIMENSIONAL STOCHASTIC DIFFERENTIAL EQUATIONS INVOLVING THE MAXIMUM PROCESS
• On stochastic differential equations

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