Numerical and mathematical analysis of blow-up problems for a stochastic differential equation

Tetsuya Ishiwata, Young Chol Yang

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the blow-up problems of the power type of stochastic differential equation, dX = αXp(t)dt + Xq(t)dW(t). It has been known that there exists a critical exponent such that if p is greater than the critical exponent then the solution X(t) blows up almost surely in the finite time. In our research, focus on this critical exponent, we propose a numerical scheme by adaptive time step and analyze it mathematically. Finally we show the numerical result by using the proposed scheme.

Original languageEnglish
Pages (from-to)909-918
Number of pages10
JournalDiscrete and Continuous Dynamical Systems - Series S
Volume14
Issue number3
DOIs
Publication statusPublished - 2021 Mar

Keywords

  • Adaptive time step control
  • Blow-up
  • Blow-up time
  • Euler-Maruyama scheme
  • SDE

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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