LIMIT LAWS FOR LOCAL-TIMES OF THE BROWNIAN SHEET

Let B(s, t), s, t>0 be a Brownian sheet. Then for all s>0, the process Bs(t){colon equals}B(s, t), t>0 is a (scaled) Brownian motion which admits a local time Ls(x; t), which is jointly continuous in x∈R and s, t>0. s1/2Ls is a standard Brownian local time. We prove that {Mathematical expression} This result has several corollaries, both for Ls and the local time of B(s, t), most of them new. The new ingredient in the proof has applications to other questions concerning local times. In particular, we give a new proof of the well known large deviations result for Brownian local time, {Mathematical expression} Previous proofs of this, unlike the present one, have relied on the techniques specific to Brownian motion. © 1990 Springer-Verlag.