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Localization results for densities associated with stable small-noise diffusions
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  • Published: March 1988

Localization results for densities associated with stable small-noise diffusions

  • Martin V. Day1 

Probability Theory and Related Fields volume 77, pages 457–470 (1988)Cite this article

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Summary

This paper concerns asymptotic properties of the stationary density associated with small-noise diffusion processes, such as considered in the well-known work of Ventcel and Freidlin [12]. We assume that the origin is a globally attracting asymptotically stable equilibrium point of the underlying deterministic flow. For a bounded domain D, containing the origin, we derive estimates which establish the asymptotic independence, as the size of the noise vanishes, of the equilibrium density in D from the coefficients of the process outside D. These results are applied to generalize a result of Sheu [10] on an asymptotic representation of the equilibrium density.

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Authors and Affiliations

  1. Department of Mathematics, Virginia Tech, 24061, Blacksburg, VA, USA

    Martin V. Day

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  1. Martin V. Day
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Day, M.V. Localization results for densities associated with stable small-noise diffusions. Probab. Th. Rel. Fields 77, 457–470 (1988). https://doi.org/10.1007/BF00319299

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  • Received: 01 August 1984

  • Revised: 20 October 1987

  • Issue Date: March 1988

  • DOI: https://doi.org/10.1007/BF00319299

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Keywords

  • Stochastic Process
  • Probability Theory
  • Diffusion Process
  • Equilibrium Point
  • Statistical Theory
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