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 -