1 Random Perturbations.- 2 Small Random Perturbations on a Finite Time Interval.- 3 Action Functional.- 4 Gaussian Perturbations of Dynamical Systems. Neighborhood of an Equilibrium Point.- 5 Perturbations Leading to Markov Processes.- 6 Markov Perturbations on Large Time Intervals.- 7 The Averaging Principle. Fluctuations in Dynamical Systems with Averaging.- 8 Random Perturbations of Hamiltonian Systems.- 9 Stability Under Random Perturbations.- 10 Sharpenings and Generalizations.- References.

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