We prove a nonstandard central limit theorem for strongly mixing stationary sequences using the "radically elementary" probability theory developed by Nelson (1987) and use this result to obtain a nonstandard Markov chain central limit theorem. An analogue of a Gaussian autoregressive process is used to illustrate how to obtain the rate of convergence. A Markov chain nonstandard functional central limit theorem is also proved under conditions similar to square integrability of the underlying martingale.
|Original language||English (US)|
|Number of pages||24|
|Journal||International Journal of Uncertainty, Fuzziness and Knowlege-Based Systems|
|State||Published - Apr 2011|
Bibliographical noteFunding Information:
The first author would like to thank FINATEC/UNB (Grant Fomento-4/09) for the partial support given during his stay at the Department of Economics, University of Brasília, while this work was being completed.
- Central limit theorem
- Markov chains
- functional CLT
- nonstandard analysis