|
|
|
| Strong laws of large numbers for second order finite nonhomogeneous Markov chains |
| Faculty of Science,Jiangsu University,Zhenjiang,Jiangsu 212013,China |
|
|
|
|
Abstract The method of martingale is used to give strong laws of large numbers on frequency occurence of the states for second order finite nonhomogenous Markov chains.First,a limit theorem for averages of the functions of k variables of second order nonhomogeneous Markov chains is established by the convergence theorem for martingale difference sequence.Then,the limit theorems existed in bibliography for averages of frequency of occurrence of two states are generized to the case of arbitrary k.Finally,as corollaries,a series of strong limit theorems for frequency of occurrence of states are obtained.
|
|
|
|
|
|
|
|
|
2009, Vol. 30 
