Numerical approximation of nonlinear neutral stochastic functional differential equations

The paper investigates numerical approximations for solution of neutral stochastic functional differential equation (NSFDE) with coefficients of the polynomial growth. The main aim is to develop the convergence in probability of Euler-Maruyama approximate solution under highly nonlinear growth condi...

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Bibliographic Details
Published in:Journal of applied mathematics & computing Vol. 41; no. 1-2; pp. 427 - 445
Main Authors: Zhou, Shaobo, Fang, Zheng
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer-Verlag 01.03.2013
Springer Nature B.V
Subjects:
Applied mathematics
Approximation
Computational Mathematics
Computational Mathematics and Numerical Analysis
Convergence
Differential equations
Dynamical systems
Mathematical analysis
Mathematical and Computational Engineering
Mathematical models
Mathematics
Mathematics and Statistics
Mathematics of Computing
Nonlinearity
Numerical analysis
Polynomials
Random variables
Stochastic models
Stochasticity
Studies
Theory of Computation
Numerical approximation
Euler-Maruyama method
Neutral stochastic functional differential equation
34F05
Polynomial growth conditions
Convergence in probability
ISSN:1598-5865, 1865-2085
Online Access:Get full text
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Summary:The paper investigates numerical approximations for solution of neutral stochastic functional differential equation (NSFDE) with coefficients of the polynomial growth. The main aim is to develop the convergence in probability of Euler-Maruyama approximate solution under highly nonlinear growth conditions. The paper removes the linear growth condition of the existing results replacing by highly nonlinear growth conditions, so the convergence criteria here may cover a wider class of nonlinear systems. Moreover, we also prove the existence-and-uniqueness of the global solutions for NSFDEs with coefficients of the polynomial growth. Finally, two examples is provided to illustrate the main theory.
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ISSN:1598-5865
1865-2085
DOI:10.1007/s12190-012-0605-5