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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)

Abstract

In this chapter we shall consider perturbations of a dynamical system
$$ {\dot x_t} = b({x_t}),\quad {{\text{x}}_{\text{0}}}{\text{ = x,}}\quad b(x) = ({b^1}(x),...,{b^r}(x))$$
(1.1)
by a white noise process or by a Gaussian process in general.

Keywords

Invariant Measure Equilibrium Position Lipschitz Condition Exit Time Stable Limit Cycle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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