Large deviations and Strassen's limit points of Brownian local time processes

✍ Scribed by Bin Chen

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 316 KB
• Volume: 34
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(96)00206-4

✦ Synopsis

Let {W(t), 0~<t < oo} be a standard Brownian motion and let {L(x,t), -oo <x <oo, 0~<t < oe} be its local time process. We establish large deviations for {L(x,t),O<~t < oe} for any fixed x and for {sup ...... L(x,t), O<~t < ~}.

Then, using these, we get some results on Strassen's law for these processes.

Kevwords." Large deviations; Brownian local time; Strassen's law

1. A large deviation

Let W:={W(t),O<~t < oc} be a standard Brownian motion. Let C0[0, 1] be the space of continuous functions on the closed interval [0, 1] which vanish at the origin. Let P,: be the probability measure on this space that corresponds to {v~W(t),O<~t<~ 1}. For fEC0[0, 1], we define l(f) by