CORRECTION TO "MARKOVIAN DECISION PROCESSES WITH RECURSIVE REWARD FUNCTIONS"

In the above article (Bull. Math. Statist. Vol. 15, No. 3-4, 79-91), in Theorem 5.1 and its Corollary we need to set Assumption (I) in addition to Assumption (II). The proof of Theorem 5.1 made in the article is incomplete. Line 3 from the bottom of page 85-line 7 from the top of page 86 should read : For T = r/N there exists a Borel measurable map f N such that EN-1ng=7rNqg(sN, aN, sN-Fi, EN7cg) —5 _fNqg(sN, aN, sN+1, ENrg)+T I K1K2 ••• KN-1 with Prig ••• 7N-1q—prob. 1 . That is, EN-17'g Elf-v-v7,1g-Fr IK,K,--• KN_1 with Prig -•• 7N-ig—prob. 1. By Assumptions (I) and (II) we have zN-14g(sN-1, aN_i, sN, EN-17'g) 7r N-igg(sN-1, aN-1, SN, E IfN,N7og+rIK,K,.•• KN_,) with Prig ••• 7N-1g—prob. 1 . . 7rN-1(1g(sN-1, aN-1, SN, E (fN,N,r1g)-Fr IK1K2••• KN-2 with Prig ••• 7rN-2q—prob. 1. Using this procedure N times will produce a Markov policy 7r* = {f1, f2, -} such that E'rg< Elf Df 2,-,f N,Nlogd-Nr = E'g+e with p—prob. 1,