A Taylor polynomial approach in approximations of solution to pantograph stochastic differential equations with Markovian switching

DOI10.1016/j.mcm.2010.08.016zbMath1211.65009OpenAlexW2091127808MaRDI QIDQ534838

Marija Milošević, Miljana Jovanović

Publication date: 10 May 2011

Published in: Mathematical and Computer Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.mcm.2010.08.016

zbMATH Keywords

Taylor approximationMarkovian switchingpantograph stochastic differential equations\(L_p\) convergencea.s. convergence

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stochastic functional-differential equations (34K50) Numerical solutions to stochastic differential and integral equations (65C30) Continuous-time Markov processes on discrete state spaces (60J27)

Related Items (16)

Existence, uniqueness, almost sure polynomial stability of solution to a class of highly nonlinear pantograph stochastic differential equations and the Euler-Maruyama approximation ⋮ Stability of highly nonlinear neutral stochastic differential delay equations ⋮ A Taylor method for stochastic differential equations with time-dependent delay via the polynomial condition ⋮ A new numerical method to solve pantograph delay differential equations with convergence analysis ⋮ On the approximations of solutions to stochastic differential equations under polynomial condition ⋮ Modified Chebyshev collocation method for pantograph-type differential equations ⋮ Highly nonlinear neutral stochastic differential equations with time-dependent delay and the Euler-Maruyama method ⋮ Almost surely exponential stability of numerical solutions for stochastic pantograph equations ⋮ Numerical approximation for nonlinear stochastic pantograph equations with Markovian switching ⋮ The existence and asymptotic estimations of solutions to stochastic pantograph equations with diffusion and Lévy jumps ⋮ Convergence of numerical solutions to stochastic differential equations with Markovian switching ⋮ Convergence and almost sure polynomial stability of the backward and forward-backward Euler methods for highly nonlinear pantograph stochastic differential equations ⋮ Taylor polynomial method and error estimation for a kind of mixed Volterra-Fredholm integral equations ⋮ Approximate solutions of hybrid stochastic pantograph equations with Levy jumps ⋮ Stability with general decay rate of hybrid neutral stochastic pantograph differential equations driven by Lévy noise ⋮ Strong convergence rate of the stochastic theta method for nonlinear hybrid stochastic differential equations with piecewise continuous arguments

Cites Work

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• Comparison principle and stability criteria for stochastic differential delay equations with Markovian switching
• Convergence of numerical solutions to stochastic pantograph equations with Markovian switching
• Existence and uniqueness of the solutions and convergence of semi-implicit Euler methods for stochastic pantograph equations
• An analytic approximation of solutions of stochastic differential delay equations with Markovian switching
• Convergence of numerical solutions to neutral stochastic delay differential equations with Markovian switching
• An approximate method via Taylor series for stochastic functional differential equations
• Continuous \(\Theta\)-methods for the stochastic pantograph equation
• An analytic approximation of solutions of stochastic differential equations
• Stochastic differential delay equations with Markovian switching
• An analytic approximate method for solving stochastic integrodifferential equations
• Stochastic Differential Equations with Markovian Switching
• On a Functional Differential Equation

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