Semiclassical Analysis and a New Result for Poisson-Lévy Excursion Measures

Ian M Davies (Swansea University)

Abstract


The Poisson-Levy excursion measure for the diffusion process with small noise satisfying the Ito equation $$ dX^{\varepsilon} = b(X^{\varepsilon}(t))dt + \sqrt\varepsilon\,dB(t) $$ is studied and the asymptotic behaviour in $\varepsilon$ is investigated. The leading order term is obtained exactly and it is shown that at an equilibrium point there are only two possible forms for this term - Levy or Hawkes-Truman. We also compute the next to leading order.

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Pages: 1283-1306

Publication Date: August 14, 2008

DOI: 10.1214/EJP.v13-513

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