Convergence and stability of the balanced Euler method for stochastic pantograph differential equations with Markovian switching

Abstract

In this paper, we concern the strong convergence and stability of the balanced Euler method for stochastic pantograph differential equations with Markovian switching (SPDEs-MS). We present the balanced Euler method of SPDEs-MS and consider its moment boundedness under polynomial growth condition plus Khasminskii-type condition. We also study its strong convergence order and its mean-square stability. Two numerical examples are given to illustrate the theoretical results.

Keywords:

• Stochastic pantograph differential equations
• Markovian switching
• balanced Euler method
• strong convergence
• stability

AMS Subject Classifications:

• 65C30
• 65C40

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The research was supported by the Natural Science Foundation of Heilongjiang Province (No. LH2022A020), the Basic scientific research expenses of colleges and universities in Heilongjiang Province (No. KYYWF-1451).