Limit theorems for a higher order time dependent
Markov chain model
P. Kokoszk
T. Kutta
D. Singh
H. Wang
Abstract:
The paper establishes a strong law of large numbers and a central
limit theorem for a sequence of dependent Bernoulli random variables
modeled as a higher order Markov chain. The model under consideration is
motivated by problems in quality control where acceptability of an item
depends on the past k
acceptability scores. Moreover, the model introduces dependence that may
evolve over time and thus advances the theory for models with time
invariant dependence. We establish explicit assumptions that incorporate
this dynamic dependence and show how it enters into the limits
describing long-term behavior of the system.
2010 AMS Mathematics Subject Classification: Primary 60F05; Secondary 60F15, 60G42.
Keywords and phrases: central limit theorem, dependent Bernoulli
observations, higher order Markov model, strong law of large numbers.