🚀 go-pugleaf

In article <1992Apr9.141813.21760@lth.se> tobias@maths.lth.se (Tobias Ryden) writes:
>Let Y_n be a Markov chain on a general state space E for which there
exists a stationary distribution v, but the initial distribution of
Y, i.e. the distribution of Y_1, need not necessarily equal v.
Under which conditions does

       N
  1   ---
  -   \
  N   /    f(Y_n) -> v(f)
      ---
      n=1

hold, where f is in L_1(v) and the convergence is w.p.1, in L_1 or in
>probability?

email bounced.  See, among many other places, RW Wolff, Stochastic modeling
and the theory of queues, section 3-6.  The theory of such averages
is considerably simpler than the theory of functions; for example
in a cyclic irreducible positive recurrent discrete time
Markov chain f may fail to converge but (1/n)sigma f (y sub i)
still converges.