TY - JOUR

T1 - Approximation of solutions of multi-dimensional linear stochastic differential equations defined by weakly dependent random variables

AU - Takahashi, Hiroshi

AU - Yoshihara, Ken Ichi

N1 - Funding Information:
The authors thank Professor R. Naz, Professor M. Torrisi, Professor I. Naeem and Professor C.W. Soh for giving an opportunity to talk in AIMS 2016 Meeting, Orlando, Florida, USA. The research is supported by JSPS KAKENHI Grant number 26800063.
Publisher Copyright:
© 2017, Hiroshi Takahashi, et al., licensee AIMS Press.

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

KW - Difference equation

KW - Euler-maruyama scheme

KW - Linear stochastic differential equation

KW - Strong invariance principle

KW - Weakly dependent random variables

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U2 - 10.3934/Math.2017.3.377

DO - 10.3934/Math.2017.3.377

M3 - Article

AN - SCOPUS:85073352406

SN - 2473-6988

VL - 2

SP - 377

EP - 384

JO - AIMS Mathematics

JF - AIMS Mathematics

IS - 3

ER -