On the global asymptotic stability and oscillation of solutions in a stochastic business cycle model

Abstract

We discuss a second order nonlinear stochastic difference equation which is constructed of a business cycle model with organized labor considered. A global asymptotic mean square stability criterion is obtained by Lyapunov function method. We also prove a theorem on the almost sure oscillation of the solutions for the difference equation with state-independent stochastic perturbations.

Keywords:

• Stochastic difference equation
• stability
• almost sure oscillation
• business cycle

AMS Subject Classifications:

• 39A21
• 39A50
• 60B10
• 60G50
• 91B70

Acknowledgements

The first author thanks the Laboratoire Paul Painlevé UMR CNRS 8524, UFR de Mathématiques, Université Lille 1, where this paper is completed during his visit from September 2014 to September 2015.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by National Natural Science Foundation of China [grant number 11101283], [grant number 11371140], [grant number 11178014]; Innovation Program of Shanghai Municipal Education Commission [grant number 13ZZ137] and China Scholarship Council.