  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.
