Stability of hybrid linear stochastic systems - a technical tool in recursive identification

Gerencsér, László and Prokaj, Vilmos (2008) Stability of hybrid linear stochastic systems - a technical tool in recursive identification. In: Proc. of the Eighteenth International symposium on Mathematical Theory of Networks and Systems (MTNS2008), Virginia Tech, Blacksburg, Virginia, USA, July 28-August 1, 2008.

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Continuous-time stochastic systems have attracted a lot of attention recently due to their wide-spread use in finance, in particular in pricing derivative products. However the description of real data in terms of such models is far from settled. The identification of continuous-time stochastic systems, in particular recursive estimation, is a basic building block for continuous-time stochastic adaptive filtering and control as well, see the works of Van Schuppen, Duncan and Pasik-Duncan. In these papers the underlying stochastic systems is essentially an AR-system, for which the recursive maximum-likelihood (RML) estimation reduces to a recursive least squares (RLSQ) estimation. Recursive estimation in the same generality has been studied by DeWolf and Wiberg, under the condition that the process is stopped if it reached the boundary of a truncation domain. A rigorous convergence theory for a restricted class of non-linear stochastic systems has been given by Levanony and Zeitouini for explicit systems. This paper is the initial step in extending the theory of Benveniste, Metivier and Priouret (BMP), developed for discrete time stochastic approximation in a Markovian setting for continuous-time linear stochastic systems. As in discrete time, also in continuous time convergence w.p.1 can not be guaranteed without resetting. We will focus on the stability analysis of state-processes generated by time-varying linear hybrid stochastic systems, allowing jumps in the dynamics and in the state. Altogether the results of these paper ensure the validity of a continuous-time extension of the highly non-trivial Condition A5 of BMP, p. 220.

Item Type: Conference or Workshop Item (Paper)
Uncontrolled Keywords: Hybrid systems; stability; recursive estimation.
Subjects: Q Science > QA Mathematics and Computer Science > QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány
Depositing User: László Gerencsér
Date Deposited: 11 Dec 2012 15:31
Last Modified: 11 Dec 2012 15:31

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