Brownian Local Times and Taboo Processes

Perturbed and Non-perturbed Brownian Taboo Processes

– In this paper we study the Brownian taboo process, which is a version of Brownian motion conditioned to stay within a finite interval, and the α-perturbed Brownian taboo process, which is an analogous version of an α-perturbed Brownian motion.We are particularly interested in the asymptotic behaviour of the supremum of the taboo process, and our main results give integral tests for upper and ...

Large deviations for local times and intersection local times of fractional Brownian motions and Riemann-Liouville processes

In this paper we prove exact forms of large deviations for local times and intersection local times of fractional Brownian motions and Riemann–Liouville processes. We also show that a fractional Brownian motion and the related Riemann–Liouville process behave like constant multiples of each other with regard to large deviations for their local and intersection local times. As a consequence of o...

The Supremum of Brownian Local Times

Local times of multifractional Brownian sheets

Denote by H(t) = (H1(t), . . . ,HN (t)) a function in t ∈ R+ with values in (0, 1) . Let {B(t)} = {B(t), t ∈ R+} be an (N, d)-multifractional Brownian sheet (mfBs) with Hurst functional H(t). Under some regularity conditions on the function H(t), we prove the existence, joint continuity and the Hölder regularity of the local times of {B(t)}. We also determine the Hausdorff dimensions of the lev...

Local times of fractional Brownian sheets

Let BH 0 = fBH 0 (t); t 2 RN+g be a real-valued fractional Brownian sheet. Consider the (N; d) Gaussian random eld BH de ned by BH(t) = (BH 1 (t); : : : ; BH d (t)) (t 2 RN+ ); where BH 1 ; : : : ; BH d are independent copies of BH 0 . In this paper, the existence and joint continuity of the local times of BH are established. Running Title: Local Times of Fractional Brownian Sheets