On the rate of convergence of Euler–Maruyama approximate solutions of stochastic differential equations with multiple delays and their confidence interval estimations

Masataka Hashimoto, Hiroshi Takahashi

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we investigate Euler–Maruyama approximate solutions of stochastic differential equations (SDEs) with multiple delay functions. Stochastic differential delay equations (SDDEs) are generalizations of SDEs. Solutions of SDDEs are influenced by both the present and past states. Because these solutions may include past information, they are not necessarily Markov processes. This makes representations of solutions complicated; therefore, approximate solutions are practical. We estimate the rate of convergence of approximate solutions of SDDEs to the exact solutions in the Lp-mean for p ≥ 2 and apply the result to obtain confidence interval estimations for the approximate solutions.

Original languageEnglish
Pages (from-to)13747-13763
Number of pages17
JournalAIMS Mathematics
Volume8
Issue number6
DOIs
Publication statusPublished - 2023

Keywords

  • Euler–Maruyama approximation
  • confidence interval
  • rate of convergence
  • stochastic differential delay equation

ASJC Scopus subject areas

  • General Mathematics

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