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APPLICATIONES MATHEMATICAE 23,4 (1996), p. 355

V. S. B O R K A R (Bangalore)

Correction to

“RECURSIVE SELF-TUNING CONTROL OF FINITE MARKOV CHAINS”

(Applicationes Math. 24 (2) (1996), 169–188)

The proof of Lemma 4.4 of the above is in error. It can, however, be easily corrected with the following modification: Set h 0 = V , which is possible. One has

n→∞ lim sup

t∈[T

n

,T

n+1

)

kZ(t) − x n (t)k = 0

(The erroneous statement in the earlier proof has t ∈ [T n , T n+1 ].) For large n, the process reset to h 0 won’t move out of its ε-neighbourhood as argued in the proof of Theorem A.1. Thus there are at most finitely many resets. The rest follows as before.

[355]

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