𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Law of the iterated logarithm for Lévy's area process composed with Brownian motion

✍ Scribed by Daniel Neuenschwander

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
268 KB
Volume
40
Category
Article
ISSN
0167-7152

No coin nor oath required. For personal study only.

✦ Synopsis

Let {A(t)}-o~~o is an independent Brownian motion. Then we prove the following local law of the iterated logarithm for the composed process {A(W(t))}t>.o:
(2)3/2/ t~o tl/2(loglog(1/t)) 3/2= "3 ~"

📜 SIMILAR VOLUMES

Strassen's local law of the iterated log
Strassen's local law of the iterated logarithm for Lévy's area
✍ Modeste N'Zi 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 288 KB

We prove a Strassen's law of the iterated logarithm at zero for L&y's area process. Contrary to the Brownian case, the time inversion argument doesn't seem to work. Here, the main tool in the proof is large deviations estimates for diffusion processes with small diffusion coefficients. Loi locale

The Lévy Area Process for the Free Brown
The Lévy Area Process for the Free Brownian Motion
✍ M. Capitaine; C. Donati-Martin 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 162 KB

In this paper, we construct a Le vy area process for the free Brownian motion and in this way, a typical geometric rough path (in the sense of T. Lyons (1998, Rev. Mat. Iberoamer. 14, 215 310)), lying above the free Brownian path. Thus, the general results of Lyons on differential equations driven b