 |
|
|
| | | | | |
|
|
|
|
|
Large Deviations for One Dimensional Diffusions with a Strong Drift
|
Jochen Voss, University of Warwick
|
Abstract
We derive a large deviation principle which describes the behaviour
of a diffusion process with additive noise under the influence of a
strong drift. Our main result is a large deviation theorem for the
distribution of the end-point of a one-dimensional diffusion with
drift θb where b is a drift function and θ a real
number, when θ converges to ∞. It transpires that the
problem is governed by a rate function which consists of two parts:
one contribution comes from the Freidlin-Wentzell theorem whereas a
second term reflects the cost for a Brownian motion to stay near a
equilibrium point of the drift over long periods of time.
|
Full text: PDF
Pages: 1479-1528
Published on: September 1, 2008
|
Bibliography
- Anderson, T. W. The integral of a symmetric unimodal function over a symmetric convex set and some probability inequalities. Proc. Amer. Math. Soc. 6, (1955). 170--176. MR0069229 (16,1005a)
- Bingham, N. H.; Goldie, C. M.; Teugels, J. L. Regular variation. Encyclopedia of Mathematics and its Applications, 27. Cambridge University Press, Cambridge, 1987. xx+491 pp. ISBN: 0-521-30787-2 MR0898871 (88i:26004)
- Birkhoff, Garrett; Rota, Gian-Carlo. Ordinary differential equations. Fourth edition. John Wiley & Sons, Inc., New York, 1989. xii+399 pp. ISBN: 0-471-86003-4 MR0972977 (90h:34001)
- Borodin, Andrei N.; Salminen, Paavo. Handbook of Brownian motion---facts and formulae. Probability and its Applications. Birkhäuser Verlag, Basel, 1996. xiv+462 pp. ISBN: 3-7643-5463-1 MR1477407 (98i:60077)
- Dembo, Amir; Zeitouni, Ofer. Large deviations techniques and applications. Second edition. Applications of Mathematics (New York), 38. Springer-Verlag, New York, 1998. xvi+396 pp. ISBN: 0-387-98406-2 MR1619036 (99d:60030)
- Gelfand, I. M.; Fomin, S. V. Calculus of variations. Revised English edition translated and edited by Richard A. Silverman Prentice-Hall, Inc., Englewood Cliffs, N.J. 1963 vii+232 pp. MR0160139 (28 #3353)
- Voss, J. Some Large Deviation Results for Diffusion Processes. PhD thesis, University of Kaiserslautern, Germany, 2004.
|
|
|
|
|
|
|
|
| | | | |
Electronic Journal of Probability. ISSN: 1083-6489 |
|
Context