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Solutions of max-plus linear equations and large deviations

Marianne Akian 1 Stéphane Gaubert 1 Vassili Kolokoltsov 2
1 MAXPLUS - Max-plus algebras and mathematics of decision
Inria Paris-Rocquencourt
2 Institute for Information Transmission Problems
Abstract : We generalise the Gärtner-Ellis theorem of large deviations theory. Our results allow us to derive large deviation type results in stochastic optimal control from the convergence of generalised logarithmic moment generating functions. They rely on the characterisation of the uniqueness of the solutions of max-plus linear equations. We give an illustration for a simple investment model, in which logarithmic moment generating functions represent risk-sensitive values.
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https://hal.inria.fr/inria-00000218
Contributor : Marianne Akian <>
Submitted on : Wednesday, September 14, 2005 - 11:26:44 AM
Last modification on : Tuesday, July 14, 2020 - 11:04:04 AM

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Marianne Akian, Stéphane Gaubert, Vassili Kolokoltsov. Solutions of max-plus linear equations and large deviations. 44th IEEE Conference on Decision and Control and European Control Conference ECC 2005 (CDC-ECC'05), Dec 2005, Seville, Spain. ⟨inria-00000218⟩

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