Stochastic Extinction, An Average Lyapunov Function Approach

2024/07/28 by Foldes, Juraj, Stacy, Declan · 3 citations
#37H20 #37H30 #60H10 #60J05 #60J25 #60J70 60F15 #92D25 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2407.19606

Abstract

We study the stability of M₀, an invariant subset of a Markov process (X_t)_{t≥ 0} on a metric space M. By building the theory of average Lyapunov functions, we formulate general criteria based on the signs of Lyapunov exponents that guarantee extinction (X_t → M₀ as t → ∞). Additionally, we provide applications to a stochastic SIS epidemic model on a network with regime-switching, a stochastic differential equation version of the Lorenz system, a general class of discrete-time ecological models, and stochastic Kolmogorov systems. In many examples we improve existing results by removing unnecessary assumptions or providing sharper criteria for the extinction.

Cited by

• Population size in stochastic multi-patch ecological models
• Dynamics of stochastic microorganism flocculation models
• Population size in stochastic discrete-time ecological dynamics

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