Persistence of small noise and random initial conditions

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

Research output: Contribution to journalArticleResearchpeer-review

Abstract

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
Volume50
Issue numberA
DOIs
Publication statusPublished - 1 Dec 2018

Keywords

  • dynamical system
  • Fluid approximation
  • small noise

Cite this

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Persistence of small noise and random initial conditions. / Baker, Jeremy; Chigansky, P.; Hamza, K.; Klebaner, F. C.

In: Advances in Applied Probability, Vol. 50, No. A, 01.12.2018, p. 67-81.

Research output: Contribution to journalArticleResearchpeer-review

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AB - 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.

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