Large deviations for diffusions on the Besov-Orlicz spaces and application. (Grandes deviations des diffusions sur les espaces de Besov-Orlicz et application.) (French) Zbl 0926.60029
The authors prove a large deviations principle in Besov-Orlicz space for diffusion processes [for the result in Hoelder space see G. Ben Arous and M. Ledoux, in: Séminaire de Probabilités XXVIII. Lect. Notes Math. 1583, 293-299 (1994; Zbl 0811.60019) and for Brownian motion in Besov space see B. Roynette, Stochastics Stochastics Rep. 43, No. 3-4, 221-260 (1993; Zbl 0808.60071)]. An application to the iterated logarithm law for Lévy’s area process is given [see also M. N’zi and M. Eddahbi, Appl. Math. 24, No. 2, 223-229 (1996; Zbl 0880.60019)].
Reviewer: Mihai Gradinaru (Nancy)
MSC:
| 60F10 | Large deviations |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 46E30 | Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) |
| 60J60 | Diffusion processes |
| 60J65 | Brownian motion |
