On exponential contraction and expansion of Markovian switching diffusions

Abstract

This paper is concerned with the exponential contraction and expansion of regime-switching diffusions. The focus is on the behavior of the distance from one solution to another solution, rather than with respect to some equilibrium point. The moment and almost sure exponential contraction and expansion are investigated. General criteria and easily verifiable conditions for the moment and almost sure exponential contraction and expansion are obtained. The contribution of the Markovian switching to the exponential contraction and expansion is revealed. Several examples together with numerical experiments are provided for demonstration. The convergence of contracting observers with noisy measurements under Markovian switching and the connection between exponential contraction and global attractivity of stochastic population systems are presented.

Keywords:

• Switching diffusions
• exponential contraction
• exponential expansion
• exponential stability

Disclosure statement

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

Additional information

Funding

This research is funded by the Vietnam National University Ho Chi Minh City (VNU-HCM), the grant number A2023-28-01.