Stability analysis of the θ-method for hybrid neutral stochastic functional differential equations with jumps

Guangjie Li and Qigui Yang

Chaos, Solitons & Fractals, 2021, vol. 150, issue C

Abstract: Few results seems to be known about the stability of numerical methods for the hybrid neutral stochastic functional differential equations with jumps (also known as the neutral stochastic functional differential equations with Markovian switching and jumps (NSFDEwMJs)). This paper mainly investigates the exponential stability (both the almost sure and the mean-square exponential stability) of the θ-method for NSFDEwMJs. Precisely, it is first illustrated that the trivial solution of the NSFDEwMJ is almost surely and mean-square exponentially stable. It is then shown that the θ-method can preserve the same conclusions of the trivial solution. Numerical examples are demonstrated to illustrate the obtained results.

Keywords: Neutral stochastic functional differential equations; Markovian switching and jumps; θ-Method; Exponential stability (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:150:y:2021:i:c:s0960077921004161

DOI: 10.1016/j.chaos.2021.111062

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