Ergodic theory for general Markov chains

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Article #194

#194

From: Tobias Ryden
Date: Thu, 09 Apr 1992 14:18

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For a stationary ergodic process X_n it is well known that

       N
  1   ---
  -   \
  N   /    f(X_n) -> E(f(X_1))
      ---
      n=1

with probability 1 and in L_1 provided E|f(X_1)| is finite. Now, 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?

All references are appreciated!

-- 
+- Tobias Ryden                          Internet: tobias@maths.lth.se
   Dept. of Mathematical Statistics      Tel:   int+46 -(0)46 104276  
   Lund Institute of Technology          Fax:   int+46 -(0)46 104623   
-- P.O. Box 118, S-221 00 Lund, Sweden

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From: tobias@maths.lth.se (Tobias Ryden)
Newsgroups: sci.math.stat
Subject: Ergodic theory for general Markov chains
Message-ID: <1992Apr9.141813.21760@lth.se>
Date: 9 Apr 92 14:18:13 GMT
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