Idempotent Analysis and Its Applications

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“…Thus, Theorems 10 and 11, in particular, contain the turnpike theorems for Markov processes. Generalization of the obtained results to the case of continuous time and general state-space is given in [33].…”

“…Let all |b ij (α, β)| be bounded by some constant C. The proof of the following simple fact can be found in [23] or [33] Proposition 5 A) If (18) holds and δ < 1/n, then B maps each ball of radius…”

“…For a more copmprehensive exposition and for historical guides, the reader is reffered to the books [41], [32], [33] and to the reviews [20], [37].…”

“…For the development of the theory of optimization processes in the spirit of stochastic processes, where the notions of optimization martingales and optimization measurability play the main role, see [45], [3] and references therein. Formally, in the case of (space and time) homogeneous processes, the connection between Markov and Bellman processes is given by the Cramer transform [3], In general, Bellman processes present a kind of semi-classical approximation to the Markov processes [33], [29]. We are not going into details in this direction, but we shall explain here shortly the connection between probability and idempotent measures, which is given by the large deviation principle.…”

Iteration of order preserving subhomogeneous maps on a cone

“…Order preserving subhomogeneous maps have been studied intensively in nonlinear Perron-Frobenius theory. They arise in various fields, such as optimal control and game theory [1,24,29], idempotent analysis [17,23], the analysis of monotone dynamical systems [15,16,18,19,32,33], and discrete event systems [4,12,13]. In this list we have quoted only a few recent works and we suggest the reader to consult [25,26] for further references.…”