Shmerling, Efraim; Hochberg, Kenneth J. Stability of stochastic jump-parameter semi-Markov linear systems of differential equations. (English) Zbl 1153.60389 Stochastics 80, No. 6, 513-518 (2008). Summary: The asymptotic stability of stochastic Itô-type jump-parameter semi-Markov systems of linear differential equations is examined. A system of integral matrix equations is derived which has the property that the existence of a positive definite solution of the system implies the asymptotic stability of the stochastic semi-Markov system. Finally, an illustrative example is presented. Cited in 4 Documents MSC: 60K15 Markov renewal processes, semi-Markov processes 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 93E03 Stochastic systems in control theory (general) 93E15 Stochastic stability in control theory 34F05 Ordinary differential equations and systems with randomness Keywords:jump-parameter system; semi-Markov process; asymptotic stability PDF BibTeX XML Cite \textit{E. Shmerling} and \textit{K. J. Hochberg}, Stochastics 80, No. 6, 513--518 (2008; Zbl 1153.60389) Full Text: DOI References: [1] Shmerling E., J. Appl. Probab. 40 pp 442– (2003) · Zbl 1031.60062 · doi:10.1239/jap/1053003555 [2] Mariton M., Jump Linear Systems in Automatic Control (1990) [3] Sworder D.D., Estimation Problems in Hybrid Systems (1999) · doi:10.1017/CBO9780511546150 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.