text: abstract
  for some families of v−geometrically ergodic markov kernels indexed by a parameter, we study
  the existence of a taylor expansion of the invariant distribution in the space of signed measures. our
  approach, which completes some previous results for the perturbation analysis of markov chains, is
  motivated by a problem in statistics: a control of the bias for the nonparametric kernel estimation in
  some locally stationary markov models. we illustrate our results with a nonlinear autoregressive process
  and a galton-watson process with immigration and time-varying parameters.