Diffusion constants and martingales for senile random walks

Details Diffusion constants and martingales for senile random walks Diffusion constants and martingales for senile random walks

2007-05-23

arxiv.org/abs/0705.3305v2

Mathematics

Probability

17 pages, LaTeX; the proof of Proposition 2.3 has been simplified, and an error in the proof of Theorem 2.4 has been corrected

Scientific paper

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.

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