Scaling limit for escapes from unstable equilibria in the vanishing noise limit: Nontrivial Jordan block case

Yuri Bakhtin, Zsolt Pajor-Gyulai

Research output: Contribution to journalArticle


We consider white noise perturbations of a nonlinear dynamical system in the neighborhood of an unstable critical point with linearization given by a Jordan block of full dimension. For the associated exit problem, we study the joint limiting behavior of the exit location and exit time, in the vanishing noise limit. The exit typically happens near one of two special deterministic points associated with the eigendirection, and we obtain several more terms in the expansion for the exit point. The leading correction term is deterministic and logarithmic in the noise magnitude, while the random remainder satisfies a scaling limit.

Original languageEnglish (US)
Article number1950022
JournalStochastics and Dynamics
Issue number3
StatePublished - Jun 1 2019



  • Exit problem
  • small noise
  • unstable equilibrium

ASJC Scopus subject areas

  • Modeling and Simulation

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