LAURENTI Luca, ABATE Alessandro, BORTOLUSSI Luca, CARDELLI Luca, ČEŠKA Milan and KWIATKOWSKA Marta. Reachability Computation for Switching Diffusions:Finite Abstractions with Certifiable and Tuneable Precision. In: Proceedings of the 20th ACM International Conference on Hybrid Systems: Computation and Control. New York: Association for Computing Machinery, 2017, pp. 5564. ISBN 9781450345903. 
Publication language:  english 

Original title:  Reachability Computation for Switching Diffusions:Finite Abstractions with Certifiable and Tuneable Precision 

Title (cs):  Vypočet Dosažitelnosti v Hybridnich Systémech:Konečná Abstrakce s Garantovanou Chybou 

Pages:  5564 

Proceedings:  Proceedings of the 20th ACM International Conference on Hybrid Systems: Computation and Control 

Conference:  ACM International Conference on Hybrid Systems: Computation and Control 

Series:  ACM 

Place:  New York, US 

Year:  2017 

ISBN:  9781450345903 

Publisher:  Association for Computing Machinery 

Keywords 

Switching diffusions; stochastic hybrid models; reachability
and safety analysis; finite abstractions; time and space dis
cretisation; numerical computations

Annotation 

We consider continuous time stochastic hybrid systems with no resets and continuous dynamics described by linear stochastic differential equations  models also known as switching diffusions. We show that for this class of models reachability (and dually, safety) properties can be studied on an abstraction defined in terms of a discrete time and finite space Markov chain (DTMC), with provable error bounds. The technical contribution of the paper is a characterization of the uniform convergence of the time discretization of such stochastic processes with respect to safety properties. This allows us to newly provide a complete and sound numerical procedure for reachability and safety computation over switching diffusions. 
BibTeX: 

@INPROCEEDINGS{
author = {Luca Laurenti and Alessandro Abate and Luca
Bortolussi and Luca Cardelli and Milan
{\v{C}}e{\v{s}}ka and Marta Kwiatkowska},
title = {Reachability Computation for Switching
Diffusions:Finite Abstractions with Certifiable
and Tuneable Precision},
pages = {5564},
booktitle = {Proceedings of the 20th ACM International Conference on
Hybrid Systems: Computation and Control},
series = {ACM},
year = {2017},
location = {New York, US},
publisher = {Association for Computing Machinery},
ISBN = {9781450345903},
language = {english},
url = {http://www.fit.vutbr.cz/research/view_pub.php?id=11368}
} 