3 papers
math.PR2019
A density for the local time of the Brox diffusion
Jonathan Gutierrez-Pavón, Carlos G. Pacheco
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 max…
math.PR2019
Inverting weak random operators
Jonathan Gutierrez-Pavón, Carlos G. Pacheco
We analyze two weak random operators, initially motivated from processes in random environment. Intuitively speaking these operators are ill-defined, but using bilinear forms one c…
math.PR2019
The killed Brox diffusion
Jonathan Gutierrez-Pavón, Carlos G. Pacheco
We carry out an study of the Brox diffusion with killing. It turns out that when leaving fixed the environment one is able to recast some theory of diffusion and differential opera…