Asymptotic boundedness and stability of solutions to hybrid stochastic differential equations with jumps and the Euler-Maruyama approximation

Wei Mao, Liangjian Hu, Xuerong Mao

Research output: Contribution to journalArticlepeer-review

10 Downloads (Pure)

Abstract

In this paper, we are concerned with the asymptotic properties and numerical analysis of the solution to hybrid stochastic differential equations with jumps. Applying the theory of M-matrices, we will study the pth moment asymptotic boundedness and stability of the solution. Under the non-linear growth condition, we also show the convergence in probability of the Euler-Maruyama approximate solution to the true solution. Finally, some examples are provided to illustrate our new results.
Original languageEnglish
Pages (from-to)1-33
Number of pages33
JournalDiscrete and Continuous Dynamical Systems - Series B
Publication statusAccepted/In press - 18 Feb 2018

Keywords

  • stochastic differential equations
  • asymptotic boundedness
  • asymptotic stability
  • numerical analysis
  • Markovian switching
  • Levy jumps

Fingerprint Dive into the research topics of 'Asymptotic boundedness and stability of solutions to hybrid stochastic differential equations with jumps and the Euler-Maruyama approximation'. Together they form a unique fingerprint.

Cite this