Solutions of max-plus linear equations and large deviations

Marianne Akian; Stéphane Gaubert; Vassili Kolokoltsov

doi:10.1109/CDC.2005.1583420

Solutions of max-plus linear equations and large deviations

Marianne Akian
, Stéphane Gaubert
, Vassili Kolokoltsov

Institute for Information Transmission Problems (RAS)

Résultats de recherche: Le chapitre dans un livre, un rapport, une anthologie ou une collection › Contribution à une conférence › Revue par des pairs

Résumé

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.

langue originale	Anglais
titre	Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Pages	7787-7792
Nombre de pages	6
Les DOIs	https://doi.org/10.1109/CDC.2005.1583420
état	Publié - 1 déc. 2005
Evénement	44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 - Seville, Espagne Durée: 12 déc. 2005 → 15 déc. 2005

Série de publications

Nom	Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Volume	2005

Une conférence

Une conférence	44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Pays/Territoire	Espagne
La ville	Seville
période	12/12/05 → 15/12/05

Accès au document

10.1109/CDC.2005.1583420

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Akian, M., Gaubert, S., & Kolokoltsov, V. (2005). Solutions of max-plus linear equations and large deviations. Dans Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 (p. 7787-7792). Article 1583420 (Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05; Vol 2005). https://doi.org/10.1109/CDC.2005.1583420

Akian, Marianne ; Gaubert, Stéphane ; Kolokoltsov, Vassili. / Solutions of max-plus linear equations and large deviations. Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05. 2005. p. 7787-7792 (Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05).

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title = "Solutions of max-plus linear equations and large deviations",

abstract = "We generalise the G{\"a}rtner-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.",

author = "Marianne Akian and St{\'e}phane Gaubert and Vassili Kolokoltsov",

year = "2005",

month = dec,

day = "1",

doi = "10.1109/CDC.2005.1583420",

language = "English",

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series = "Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05",

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booktitle = "Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05",

note = "44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 ; Conference date: 12-12-2005 Through 15-12-2005",

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Akian, M , Gaubert, S & Kolokoltsov, V 2005, Solutions of max-plus linear equations and large deviations. Dans Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05., 1583420, Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05, VOL. 2005, p. 7787-7792, 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05, Seville, Espagne, 12/12/05. https://doi.org/10.1109/CDC.2005.1583420

Solutions of max-plus linear equations and large deviations. / Akian, Marianne ; Gaubert, Stéphane; Kolokoltsov, Vassili.
Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05. 2005. p. 7787-7792 1583420 (Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05; Vol 2005).

Résultats de recherche: Le chapitre dans un livre, un rapport, une anthologie ou une collection › Contribution à une conférence › Revue par des pairs

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T1 - Solutions of max-plus linear equations and large deviations

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PY - 2005/12/1

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N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/33847200828

U2 - 10.1109/CDC.2005.1583420

DO - 10.1109/CDC.2005.1583420

M3 - Conference contribution

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SN - 0780395689

SN - 9780780395688

T3 - Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05

SP - 7787

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BT - Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05

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Akian M , Gaubert S, Kolokoltsov V. Solutions of max-plus linear equations and large deviations. Dans Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05. 2005. p. 7787-7792. 1583420. (Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05). doi: 10.1109/CDC.2005.1583420

Solutions of max-plus linear equations and large deviations

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