Home | Contents | Submissions, editors, etc. | Login | Search | ECP
 Electronic Journal of Probability > Vol. 13 (2008) > Paper 45 open journal systems 


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.


Full text: PDF

Pages: 1283-1306

Published on: August 14, 2008


Bibliography
  1. Lévy, Paul. Processus stochastiques et mouvement brownien.(French) Suivi d'une note de M. Loève. Deuxième édition revue et augmentée Gauthier-Villars & Cie, Paris 1965 vi+438 pp. MR0190953 (32 #8363)
  2. Hawkes, J.; Truman, A. Statistics of local time and excursions for the Ornstein-Uhlenbeck process. Stochastic analysis (Durham, 1990), 91--101, London Math. Soc. Lecture Note Ser., 167, Cambridge Univ. Press, Cambridge, 1991. MR1166408 (93f:60117)
  3. Truman, A.; Williams, D. Excursions and Itô Calculus in Nelson's Stochastic Mechanics, ``Recent Developments in Quantum Mechanics", (Kluwer Academic Publishers, Netherlands, 1991)
  4. Davies, Ian; Truman, Aubrey. Laplace asymptotic expansions of conditional Wiener integrals and generalized Mehler kernel formulas. J. Math. Phys. 23 (1982), no. 11, 2059--2070. MR0680002 (85d:81045a)
  5. Davies,I. M; Truman, A. Semiclassical analysis and a new result in in excursion theory, in ``Probability Theory and Mathematical Statistics, Proceedings of the Seventh Vilnius Conference (1998)'', edited by B. Grigelionis et al, (Utrecht: VSP, Vilnius: TEV, 1999), 701 -- 706
  6. Olver, F. W. J. Asymptotics and special functions.Computer Science and Applied Mathematics.Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1974. xvi+572 pp. MR0435697 (55 #8655)
















Research
Support Tool
Capture Cite
View Metadata
Printer Friendly
Context
Author Address
Action
Email Author
Email Others


Home | Contents | Submissions, editors, etc. | Login | Search | ECP

Electronic Journal of Probability. ISSN: 1083-6489