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

Hiroshi Takahashi, Ken Ichi Yoshihara

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)377-384
Number of pages8
JournalAIMS Mathematics
Volume2
Issue number3
DOIs
Publication statusPublished - 2017
Externally publishedYes

Keywords

  • Difference equation
  • Euler-maruyama scheme
  • Linear stochastic differential equation
  • Strong invariance principle
  • Weakly dependent random variables

ASJC Scopus subject areas

  • Mathematics(all)

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