Abrupt convergence for stochastic small perturbations of one dimensional dynamical systems

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We study the cut-off phenomenon for a family of stochastic small perturbations
of a one dimensional dynamical system. We will focus in a semiflow of a deterministic differential equation which is perturbed by adding to the dynamics a white noise of small variance. Under suitable hypothesis on the potential we will prove that the family of perturbed stochastic differential equations present a profile cut-off phenomenon with respect to the total variation distance. We also prove a local cut-off phenomenon in a neighborhood of the local minima (metastable states) of multi-well potential.
Original languageEnglish
JournalJournal of Statistical Physics
Issue number1
Pages (from-to)113-138
Number of pages26
Publication statusPublished - 2016
MoE publication typeA1 Journal article-refereed

Fields of Science

  • 111 Mathematics
  • Perturbed dynamical systems
  • 112 Statistics and probability
  • Stochastic differential equations
  • Total variation distance
  • 114 Physical sciences
  • Cut-off phenomenon
  • Brownian motion

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