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

   
@article{EJP513,
	author = {Ian Davies},
	title = {Semiclassical Analysis and a New Result for Poisson-Lévy Excursion Measures},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {13},
	year = {2008},
	keywords = {excursion measures, asymptotic expansions},
	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.},
	pages = {no. 45, 1283-1306},
	issn = {1083-6489},
	doi = {10.1214/EJP.v13-513},    
        url = {http://ejp.ejpecp.org/article/view/513}}