Diffusion constants and martingales for senile random walks
Probability
2007-11-19 v2
Abstract
We derive diffusion constants and martingales for senile random walks with the help of a time-change. We provide direct computations of the diffusion constants for the time-changed walks. Alternatively, the values of these constants can be derived from martingales associated with the time-changed walks. Using an inverse time-change, the diffusion constants for senile random walks are then obtained via these martingales. When the walks are diffusive, weak convergence to Brownian motion can be shown using a martingale functional limit theorem.
Cite
@article{arxiv.0705.3305,
title = {Diffusion constants and martingales for senile random walks},
author = {Wouter Kager},
journal= {arXiv preprint arXiv:0705.3305},
year = {2007}
}