Journal of the Korean Mathematical Society (대한수학회지)
- Volume 33 Issue 4
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- Pages.983-992
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- 1996
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- 0304-9914(pISSN)
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- 2234-3008(eISSN)
LIMIT THEOREMS FOR MARKOV PROCESSES GENERATED BY ITERATIONS OF RANDOM MAPS
Abstract
Let p(x, dy) be a transition probability function on $(S, \rho)$, where S is a complete separable metric space. Then a Markov process $X_n$ which has p(x, dy) as its transition probability may be generated by random iterations of the form $X_{n+1} = f(X_n, \varepsilon_{n+1})$, where $\varepsilon_n$ is a sequence of independent and identically distributed random variables (See, e.g., Kifer(1986), Bhattacharya and Waymire(1990)).
Keywords
- Markov process;
- invariant probability;
- weak convergence;
- strong law of large numbers;
- functional central limit theorem