Approximations of Euler-Maruyama type for stochastic differential equations with Markovian switching, under non-Lipschitz conditions

DOI10.1016/j.cam.2006.01.052zbMath1121.65011OpenAlexW2054324811MaRDI QIDQ885945

Xuerong Mao, Chenggui Yuan, G. George Yin

Publication date: 14 June 2007

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

Full work available at URL: https://doi.org/10.1016/j.cam.2006.01.052

zbMATH Keywords

stochastic differential equationconvergenceBrownian motionMarkov chainnon-Lipschitz conditionEuler-Maruyama method

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Brownian motion (60J65) Ordinary differential equations and systems with randomness (34F05) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)

Related Items (28)

Numerical method of highly nonlinear and nonautonomous neutral stochastic differential delay equations with Markovian switching ⋮ On the approximations of solutions to neutral SDEs with Markovian switching and jumps under non-Lipschitz conditions ⋮ Tamed-Euler method for nonlinear switching diffusion systems with locally Hölder diffusion coefficients ⋮ Stabilization for a class of continuous‐time nonlinear Markov jump systems via the approximate discrete‐time model ⋮ Asymptotic mean‐square boundedness of the numerical solutions for stochastic complex‐valued neural networks with jumps ⋮ Weak Convergence of Path-Dependent SDEs in Basket Credit Default Swap Pricing with Contagion Risk ⋮ Strong convergence of the tamed Euler method for nonlinear hybrid stochastic differential equations with piecewise continuous arguments ⋮ Pathwise convergence rates for numerical solutions of Markovian switching stochastic differential equations ⋮ Existence and uniqueness of stochastic differential equations with random impulses and Markovian switching under non-Lipschitz conditions ⋮ Finite‐time stabilization of Markovian switched stochastic high‐order nonlinear systems with inverse dynamics ⋮ Exponential synchronization of delayed neutral-type neural networks with Lévy noise under non-Lipschitz condition ⋮ Approximations of numerical method for neutral stochastic functional differential equations with Markovian switching ⋮ Reliability analysis of wireless sensor networks using Markovian model ⋮ Analytic approximation of the solutions of stochastic differential delay equations with Poisson jump and Markovian switching ⋮ Invariant Measures and Euler--Maruyama's Approximations of State-Dependent Regime-Switching Diffusions ⋮ Tamed-Euler method for hybrid stochastic differential equations with Markovian switching ⋮ Permanence and asymptotical behavior of stochastic prey-predator system with Markovian switching ⋮ Convergence of numerical solutions to stochastic differential equations with Markovian switching ⋮ Strong convergence of explicit schemes for highly nonlinear stochastic differential equations with Markovian switching ⋮ Strong convergence rates for backward Euler–Maruyama method for non-linear dissipative-type stochastic differential equations with super-linear diffusion coefficients ⋮ Mixture dynamics and regime switching diffusions with application to option pricing ⋮ Strong Solutions of a Class of Stochastic Differential Equations with Jumps ⋮ Convergence rate of numerical solutions for nonlinear stochastic pantograph equations with Markovian switching and jumps ⋮ Continuous dependence for stochastic functional differential equations with state-dependent regime-switching on initial values ⋮ Pinning synchronization of time-varying polytopic directed stochastic networks ⋮ Numerical solutions of SDEs with Markovian switching and jumps under non-Lipschitz conditions ⋮ Strong convergence rate of the stochastic theta method for nonlinear hybrid stochastic differential equations with piecewise continuous arguments ⋮ Pricing exotic options using MSL-MC

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Higher-order implicit strong numerical schemes for stochastic differential equations
• Necessary and sufficient condition for robust stability and stabilizability of continuous-time linear systems with Markovian jumps
• Convergence of the Euler--Maruyama method for stochastic differential equations with Markovian switching.
• Stability of stochastic differential equations with Markovian switching
• A Theory of the Term Structure of Interest Rates
• Stochastic stability properties of jump linear systems
• Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations
• A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options
• Some remarks on the duality of continuous time markov chains
• Stochastic Equations in Infinite Dimensions

This page was built for publication: Approximations of Euler-Maruyama type for stochastic differential equations with Markovian switching, under non-Lipschitz conditions