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

Wei Mao, Liangjian Hu, Xuerong Mao

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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

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