Variable Length Markov Chains, Persistent Random Walks: A Close Encounter

Limit theorems for chains with unbounded variable length memory which satisfy Cramer condition

“…But here we would like to mention the class of processes known in the literature as a Persistent random walk (PRW), a Goldstein-Kac random walk, or also a correlated random walk, see [9] for definitions and short historical introduction. The increments of these random walks are not independent but form a Markov chain and are closely related to the chains with unbounded variable length memory, see [9,10]. These random walks can be considered as a chain with unbounded variable length memory with the special context tree on the binary alphabet called by the authors as a double (infinite) comb context tree [9].…”