Asymptotic behaviour of the utility vector in a dynamic programming model

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In mathematical economics (e.g. Leontief substitution systems) and in Markov decision theory we often deal with dynamic programming recursions of the following form $ x(n+1) = \max_{P \in M} Px(n) ; n = 0,1,2,... $ where x(0) is assumed to be a strictly positive vector. M is a set of matrices, generated by all possible interchanges of corresponding rows, taken from a fixed finite set of nonnegative square matrices (not necessarily stochastic). We investigate the asymptotic behaviour of the vector x(n) in terms of generalized eigenvectors of a particular matrix $P ]in M$, with respect to its spectral radius $\sigma(P)$. This paper extends earlier results of Sladky [11] and Zijm [13].
Originele taal-2Engels
Plaats van productieEindhoven
UitgeverijTechnische Hogeschool Eindhoven
Aantal pagina's18
StatusGepubliceerd - 1980

Publicatie series

NaamMemorandum COSOR
Volume8004
ISSN van geprinte versie0926-4493

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