Keywords
- Stochastic Reachability
- Reachability Analysis
- Bujorianu
- Stochastic Hybrid Systems
- 44th IEEE Conference Decision
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The online version of the original chapter: Markov Models can be found at doi:10.1007/978-1-4471-2795-6_2.
The online version of the original chapter: Stochastic Reachability Concepts can be found at doi:10.1007/978-1-4471-2795-6_5.
The online version of the original chapter: Stochastic Reachability with Constraints can be found at doi:10.1007/978-1-4471-2795-6_10.
The online version of the original chapter: Applications of Stochastic Reachability can be found at doi:10.1007/978-1-4471-2795-6_11.
The online version of book back matter can be found at doi:10.1007/978-1-4471-2795-6.
Erratum to: Markov Models, pp. 5–29 DOI 10.1007/978-1-4471-2795-6_2
Pg. 29
This chapter represents a quick tour from the theory of discrete Markov processes to continuous ones. The material presented here is common knowledge and introduced following a standard manner. The reader interested in more detail presentations is referred to the well-known monographs (for Markov chains, see [229, 230], for continuous processes, see [231]). However, most tutorials (online or printed) have similar content.
The connections between the theory of Markov processes and the potential theory (characterisations based on operator semigroups, operator resolvent excessive/harmonic functions) have a long history and go back to Kakutani 1944. We give here only highlights, but for the interested reader there exist modern textbooks that treat these in details, like [232].
We give in this chapter the necessary background for understanding this book, but also other author’s contributions in the field of hybrid systems that have not been included in this volume, for example [233, 234, 235]. They will be included in a follow up volume with multiple authors.
Erratum to: Stochastic Reachability Concepts, pp. 87–103 DOI 10.1007/978-1-4471-2795-6_5
Pg. 93
Fig. 5.1: There is a repetition of “Hitting distributions”.
Erratum to: Stochastic Reachability with Constraints, pp. 187–202 DOI 10.1007/978-1-4471-2795-6_10
Pg. 185
The results regarding stochastic bisimulation presented in this chapter have been reported first in [236].
Erratum to: Applications of Stochastic Reachability, pp. 203–207 DOI 10.1007/978-1-4471-2795-6_11
Pg. 202
The results regarding state-constrained reachability presented in this chapter have been reported first in [237, 238].
Erratum to: Book Back Matter, pp. 209–244 DOI 10.1007/978-1-4471-2795-6
Pg. 242 (References)
229. Kemeny, J.G., Snell, J.L.: Finite Markov Chains. Van Nostrand (1960) (210 pp.)
230. Kemeny, J.G., Snell, J.L, Knapp, A.W.: Denumerable Markov Chains. Springer (1976) (500 pp.)
231. Gardiner, C.W.: Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences, 4th edn. Series in Synergetics, vol. 13. Springer (1997)
232. Kolokoltsov, V.N.: Markov Processes, Semigroups and Generators. De Gruyter Studies in Mathematics, vol. 38. De Gryuter (2011) (430 pp.)
233. Bujorianu, M.L., Lygeros, J., Bujorianu, M.C.: Bisimulation for stochastic hybrid systems. In: Morari, M., Thiele, L. (eds.) Proceedings Hybrid Systems: Computation and Control, 8th International Workshop, HSCC 2005. Springer Lecture Notes in Computer Science, vol. 3414, pp. 198–216 (2005).
234. Bujorianu, M.L., Bujorianu, M.C.: A Model Checking Strategy for a Performance Measure of Fluid Stochastic Models. Springer Lecture Notes in Computer Science, vol. 4054, pp. 93–107 (2006).
235. Bujorianu, M.L., Bujorianu, M.C., Barringer, H.: A Formal Framework for User-Centric Control of Multi-agent Cyber-physical Systems. Lecture Notes in Artificial Intelligence, vol. 5405, pp. 97–116 (2009).
236. Bujorianu, M.L., Bujorianu, M.C., Lygeros, J.: Abstractions of stochastic hybrid systems. In: 44th IEEE Conference Decision and Control, and European Control Conference. CDC-ECC ’05, pp. 4712–4717 (2005).
237. Bujorianu, M.L., Bujorianu, M.C.: State constrained reachability analysis of stochastic hybrid systems. In: Proceedings of Analysis and Design of Hybrid Systems ADHS 2009, pp. 168–173. Elsevier Press.
238. Bujorianu, M.L., Bujorianu, M.C.: Constrained stochastic reachability for stochastic hybrid systems. J. Nonlinear Anal. Hybrid Syst. 5(2), 320–342 (2011).
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Bujorianu, L.M. (2012). Stochastic Reachability Analysis of Hybrid Systems. In: Stochastic Reachability Analysis of Hybrid Systems. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-2795-6_12
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