Continuous-time ballistic process with random resets

We consider ballistic motion on the line with random velocity which at certain random epochs of time is reset to its starting position. The mobile then restarts from scratch with new velocity, sampled with a certain probability distribution, until the next reset occurs. The distribution for the hitt...

Full description

Saved in:
Bibliographic Details
Published in:Journal of statistical mechanics 2018-12, Vol.2018 (12), p.123204
Main Authors: Villarroel, Javier, Montero, Miquel
Format: Article
Language:English
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We consider ballistic motion on the line with random velocity which at certain random epochs of time is reset to its starting position. The mobile then restarts from scratch with new velocity, sampled with a certain probability distribution, until the next reset occurs. The distribution for the hitting time to an arbitrary level is obtained. Inversion of the relevant Laplace transform is discussed under particular choices for the distribution of velocities and resets train and classified in terms of the weights of reset and velocities tails. The large time behavior of the running-maximum is considered.
ISSN:1742-5468
1742-5468
DOI:10.1088/1742-5468/aaeb47