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A Calculus of Stochastic Systems : Specification, Simulation, and Hidden State Estimation

Albert Benveniste 1 Bernard Levy 2 Eric Fabre 1 Paul Le Guernic 3
1 AS - Signal Processing and Control
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, INRIA Rennes
3 EP-ATR - Environnement de programmation d'applications temps réel
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, INRIA Rennes
Abstract : In this paper, we consider {\it hybrid systems} containing both stochastic and \deterministic components. To compose such systems, we introduce a general combinator which allows the specification of an arbitrary hybrid system in terms of elementary components of only two types. Thus, systems are obtained hierarchically, by composing subsystems, where each subsystem can be viewed as an "increment" in the decomposition of the full system. The resulting hybrid stochastic system specifications are generally not "executable", since they do not necessarily permit the incremental simulation of the system variables. Such a simulation requires compiling the dependency relations existing between the system variables. Another issue involves finding the most likely internal states of a stochastic system from a set of observations. We provide a small set of primitives for transforming hybrid systems, which allows the solution of the two problems of incremental simulation and estimation of stochastic systems within a common framework. The complete model is called CSS ({\it a Calculus of Stochastic Systems}), and is implemented by the \si language, derived from the \signal synchronous language. Our results are applicable to pattern recognition problems formulated in terms of Markov random fields or hidden Markov models (HMMs), and to the automatic generation of diagnostic systems for industrial plants starting from their risk analysis.
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https://hal.inria.fr/inria-00074210
Contributor : Rapport de Recherche Inria <>
Submitted on : Wednesday, May 24, 2006 - 2:45:26 PM
Last modification on : Friday, February 12, 2021 - 3:33:14 AM
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  • HAL Id : inria-00074210, version 1

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Albert Benveniste, Bernard Levy, Eric Fabre, Paul Le Guernic. A Calculus of Stochastic Systems : Specification, Simulation, and Hidden State Estimation. [Research Report] RR-2465, INRIA. 1994. ⟨inria-00074210⟩

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