Highly nonlinear neutral stochastic differential equations with time-dependent delay and the Euler–Maruyama method

The subject of this paper is the development of discrete-time approximations for solutions of a class of highly nonlinear neutral stochastic differential equations with time-dependent delay. The main contribution is to establish the convergence in probability of the Euler–Maruyama approximate soluti...

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Vydané v:Mathematical and computer modelling Ročník 54; číslo 9; s. 2235 - 2251
Hlavný autor: MILOSEVIC, Marija
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Kidlington Elsevier Ltd 01.11.2011
Elsevier
Predmet:
Convergence in probability
equations
Euler–Maruyama method
Exact sciences and technology
Khasminskii-type conditions
Mathematical analysis
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Neutral stochastic differential equations
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in probability and statistics
probability
Sciences and techniques of general use
Sequences, series, summability
Time-dependent delay
Euler–Maruyama method
Neutral stochastic differential equations
Khasminskii-type conditions
Time-dependent delay
Convergence in probability
Solution uniqueness
Euler-Maruyama method
Existence condition
Differential equation
Probability distribution
Delay equation
Euler scheme
Discrete scheme
Convergence
Exact solution
Non linear equation
Neutral equation
Applied mathematics
Discrete time
Integral equation
Mathematical model
Computer aided analysis
Stochastic equation
ISSN:0895-7177, 1872-9479
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Popis
Shrnutí:The subject of this paper is the development of discrete-time approximations for solutions of a class of highly nonlinear neutral stochastic differential equations with time-dependent delay. The main contribution is to establish the convergence in probability of the Euler–Maruyama approximate solution without the linear growth condition, that is, under Khasminskii-type conditions. The presence of the delayed argument in the equation, especially in the derivative of the state variable, requires a special treatment and some additional conditions, except the conditions that guarantee the existence and uniqueness of the exact solution. The existence and uniqueness result and the convergence in probability are directly influenced by the properties of the delay function.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 23
ISSN:0895-7177
1872-9479
DOI:10.1016/j.mcm.2011.05.033