The Supremum of Brownian Local times on Hölder Curves

THE SUPREMUM OF BROWNIAN LOCAL TIMES ON HÖLDER CURVES LE SUPREMUM DU TEMPS LOCAUX D’UN MOUVEMENT BROWNIEN SUR LES COURBES HOLDERIENNES Short title: Brownian local times

For f : [0, 1]→ R, we consider Lft , the local time of spacetime Brownian motion on the curve f . Let Sα be the class of all functions whose Hölder norm of order α is less than or equal to 1. We show that the supremum of Lf1 over f in Sα is finite is α > 12 and infinite if α < 1 2 . Abstrait: Soit Wt un mouvement brownien et soit L f t le temps local du processus (t,Wt) pour le courbe f : [0, 1...

The Supremum of Brownian Local Times

Ten penalisation results of Brownian motion involving its one-sided supremum until first and last passage times, VIII

We penalise Brownian motion by a function of its one-sided supremum considered up to the last zero before t, resp. first zero after t, of that Brownian motion. This study presents some analogy with penalisation by the longest length of Brownian excursions, up to time t.

The integral of the supremum process of Brownian motion

In this paper we study the integral of the supremum process of standard Brownian motion. We present an explicit formula for the moments of the integral (or area) A(T ), covered by the process in the time interval [0, T ]. The Laplace transform of A(T ) follows as a consequence. The main proof involves a double Laplace transform of A(T ) and is based on excursion theory and local time for Browni...

Effects of Brownian motion and Thermophoresis on MHD Mixed Convection Stagnation-point Flow of a Nanofluid Toward a Stretching Vertical Sheet in Porous Medium

This article deals with the study of the two-dimensional mixed convection magnetohydrodynamic (MHD) boundary layer of stagnation-point flow over a stretching vertical plate in porous medium filled with a nanofluid. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis in the presence of thermal radiation. The skin-friction coefficient, Nusselt number an...