Brownian local times

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

The Distribution of Local times of a Brownian Bridge the Distribution of Local times of a Brownian Bridge

Stochastically gated local and occupation times of a Brownian particle.

We generalize the Feynman-Kac formula to analyze the local and occupation times of a Brownian particle moving in a stochastically gated one-dimensional domain. (i) The gated local time is defined as the amount of time spent by the particle in the neighborhood of a point in space where there is some target that only receives resources from (or detects) the particle when the gate is open; the tar...