Limit theorems for reinforced random walks on certain trees
The author studies limit theorems for reinforced random walks on certain trees. For instance, in case \(X\) is any process on the \(b\)-ary tree and \(L(\nu,k)\) is the number of times \(X\) jumped from \(\nu\) to one of its children or vice versa, by time \(k\), then the strong law is proved by putting a bound condition on \(L(\rho,T_n)\), where \(T_n= \text{inf}\{k:|X_\mu|= n\}\).
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