  Adaptive Markov Chain Monte Carlo (AMCMC) is a class of MCMC algorithms where
the proposal distribution changes at every iteration of the chain. In this case
it is important to verify that such a Markov Chain indeed has a stationary
distribution. In this paper we discuss a diffusion approximation to a discrete
time AMCMC. This diffusion approximation is different when compared to the
diffusion approximation as in Gelman, Gilks and Roberts (1997) where the state
space increases in dimension to infinity. In our approach the time parameter is
sped up in such a way that the limiting distribution (as the mesh size goes to
0) is to a non-trivial continuous time diffusion process.
