A density for the local time of the Brox diffusion

2019/09/13 by Gutierrez-Pavón, Jonathan, Pacheco, Carlos G.
#60G07 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1909.06290

Abstract

We give explictly the probability density of the local time of the Brox diffusion at first passage times. Such formula is used to find the moments and to related the minima and maxima of the environment to the most and least visted points of the diffusion.

Related

• Limit law of the local time for Brox's diffusion
• Almost sure asymptotics for the maximum local time in Brownian environment
• Estimation of first passage time densities of diffusions processess\n through time-varying boundaries
• The killed Brox diffusion
• Quenched and annealed heat kernel estimates for Brox's diffusion