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• W3098604688 abstract "We introduce the notion of Lyapunov exponents for random dynamical systems, conditioned to trajectories that stay within a bounded domain for asymptotically long times. This is motivated by the desire to characterize local dynamical properties in the presence of unbounded noise (when almost all trajectories are unbounded). We illustrate its use in the analysis of local bifurcations in this context. The theory of conditioned Lyapunov exponents of stochastic differential equations builds on the stochastic analysis of quasi-stationary distributions for killed processes and associated quasi-ergodic distributions. We show that conditioned Lyapunov exponents describe the local stability behaviour of trajectories that remain within a bounded domain and - in particular - that negative conditioned Lyapunov exponents imply local synchronisation. Furthermore, a conditioned dichotomy spectrum is introduced and its main characteristics are established." @default.
• W3098604688 created "2020-11-23" @default.
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• W3098604688 date "2019-05-20" @default.
• W3098604688 modified "2023-10-10" @default.
• W3098604688 title "Conditioned Lyapunov exponents for random dynamical systems" @default.
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• W3098604688 doi "https://doi.org/10.1090/tran/7803" @default.
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