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Stochastic Newton equation in strong potential limit

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  • Liang, Song

Abstract

We consider a type of stochastic Newton equations, with single-well potential functions, and study the limiting behaviors of their solution processes when the coefficients of the potentials diverge to infinity. We prove that for dimension 1, the stochastic solution processes converge. The explicit descriptions of the limiting processes are also given. Especially, the limiting processes are deterministic for special initial conditions.

Suggested Citation

  • Liang, Song, 2016. "Stochastic Newton equation in strong potential limit," Stochastic Processes and their Applications, Elsevier, vol. 126(10), pages 2913-2955.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:10:p:2913-2955
    DOI: 10.1016/j.spa.2016.03.007
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    1. Albeverio, Sergio & Smii, Boubaker, 2015. "Asymptotic expansions for SDE’s with small multiplicative noise," Stochastic Processes and their Applications, Elsevier, vol. 125(3), pages 1009-1031.
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