Persistence of small noise and random initial conditions

Jeremy Baker, P. Chigansky, K. Hamza, F. C. Klebaner

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The effect of small noise in a smooth dynamical system is negligible on any finite time interval; in this paper we study situations where the effect persists on intervals increasing to. Such an asymptotic regime occurs when the system starts from an initial condition that is sufficiently close to an unstable fixed point. In this case, under appropriate scaling, the trajectory converges to a solution of the unperturbed system started from a certain random initial condition. In this paper we consider the case of one-dimensional diffusions on the positive half-line; this case often arises as a scaling limit in population dynamics.

Original languageEnglish
Pages (from-to)67-81
Number of pages15
JournalAdvances in Applied Probability
Issue numberA
Publication statusPublished - 1 Dec 2018


  • dynamical system
  • Fluid approximation
  • small noise

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