Sample Paths and Limit Theorems
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those which are based upon the existence of martingales associated with the chain;
the Strong Law of Large Numbers (LLN), which states that n-1Sn(g) converges to π (g) = E π[g(Φ0)], the steady state expectation of g(Φ0) ;
the Central Limit Theorem (CLT) , which states that the sum Sn(g-π(g)), when properly normalized, is asymptotically normally distributed;
the Law of the Iterated Logarithm (LIL) which gives precise upper and lower bounds on the limit supremum of the sequence Sn(g-π(g)) again when properly normalized.
KeywordsMarkov Chain Harmonic Function Central Limit Theorem Poisson Equation Sample Path
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