A continuous dynamical system generated by a vector field and
perturbed by white noise will be discussed. We shall consider an
unstable equilibrium point and obtain the asymptotics of exit times
for its neighborhood in the limit of vanishing intensity of the noise.
We shall also consider a family of hyperbolic equilibrium points
connected by heteroclinic orbits, and discuss conditions leading to
Markov and non-Markov dynamics on these hyperbolic fixed points in the
limit of vanishing noise intensity.

Lecture #13325

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