Semiclassical analysis and a new result for Poisson-Lévy excursion measures
Ian M Davies, Swansea University
Abstract
The Poisson-Lévy excursion measure for the diffusion process with small noise
satisfying the Itô equation
dXε = b(Xε(t))dt +
√ε dB(t)
is studied and the asymptotic behaviour in ε 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 - Lévy or Hawkes—Truman. We also compute
the next to leading order term and demonstrate the remarkable fact that it is identically zero.
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