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Approximation of solutions of multi-dimensional linear stochastic differential equations defined by weakly dependent random variables
- Source :
- AIMS Mathematics, Vol 2, Iss 3, Pp 377-384 (2017)
- Publication Year :
- 2017
- Publisher :
- AIMS Press, 2017.
-
Abstract
- It is well-known that under suitable conditions there exists a unique solution of a ddimensional linear stochastic differential equation. The explicit expression of the solution, however, is not given in general. Hence, numerical methods to obtain approximate solutions are useful for such stochastic di erential equations. In this paper, we consider stochastic difference equations corresponding to linear stochastic differential equations. The difference equations are constructed by weakly dependent random variables, and this formulation is raised by the view points of time series. We show a convergence theorem on the stochastic difference equations.
- Subjects :
- Independent equation
Differential equation
General Mathematics
lcsh:Mathematics
Mathematical analysis
Malliavin calculus
lcsh:QA1-939
Stochastic partial differential equation
Examples of differential equations
symbols.namesake
Stochastic differential equation
Nonlinear system
Runge–Kutta method
symbols
Difference equation| weakly dependent random variables| Euler-Maruyama scheme| strong invariance principle| linear stochastic di erential equation
Mathematics
Subjects
Details
- Language :
- English
- ISSN :
- 24736988
- Volume :
- 2
- Issue :
- 3
- Database :
- OpenAIRE
- Journal :
- AIMS Mathematics
- Accession number :
- edsair.doi.dedup.....e666595b04c1654e32e44638703821fd