Gaussian Perturbations of Dynamical Systems. Neighborhood of an Equilibrium Point

  • M. I. Freidlin
  • A. D. Wentzell
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 260)


In this chapter we shall consider perturbations of a dynamical system
$$ {\dot x_t} = b({x_t}),\quad {{\text{x}}_{\text{0}}}{\text{ = x,}}\quad b(x) = ({b^1}(x),...,{b^r}(x))$$
by a white noise process or by a Gaussian process in general.


Invariant Measure Equilibrium Position Lipschitz Condition Exit Time Stable Limit Cycle 
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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • M. I. Freidlin
    • 1
  • A. D. Wentzell
    • 2
  1. 1.Department of MathematicsUniversity of MarylandCollege ParkUSA
  2. 2.Department of MathematicsTulane UniversityNew OrleansUSA

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