Abstract
We consider MDPs and CMs with structured state space and arbitrary transition law. We assume that the minimal assumption (MA1) holds. As in Chap. 6 we are looking for conditions under which the value functions are monotone in the initial state s. This is easy for CMs, but requires a thorough treatment of the notion of stochastic monotonicity for MDPs. Unless stated otherwise, a result holds for both MDPs and CMs.
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References
Karlin, S., & Rinott, Y. (1980). Classes of orderings of measures and related correlation inequalities. II. Multivariate reverse rule distributions. Journal of Multivariate Analysis, 10, 499–516.
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© 2016 Springer International Publishing AG
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Hinderer, K., Rieder, U., Stieglitz, M. (2016). Stochastic Monotonicity and Monotonicity of the Value Functions. In: Dynamic Optimization. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-319-48814-1_18
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DOI: https://doi.org/10.1007/978-3-319-48814-1_18
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-48813-4
Online ISBN: 978-3-319-48814-1
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