A concept of 'near invariance' is developed starting from sets that are
actually invariant under smaller perturbations. This is based on a
theory for system dynamics of Markov diffusion processes illuminating
the idea of 'large' noise perturbations turning invariant sets for
smaller noise ranges into transient sets. This also allows for numerical
computation of nearly invariant sets, the exit times from these sets,
and the exit locations under varying perturbation ranges. The
controllability behavior of associated deterministic systems plays a
crucial role. Several examples will be discussed.

Lecture #13331

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