No abstract

This report presents the results of a friendly competition for formal verification and policy synthesis of stochastic models. It also introduces new benchmarks within this category, and recommends next steps for this category towards next year’s edition of the competition. The friendly competition took place as part of the workshop Applied Verification for Continuous and Hybrid Systems (ARCH) in Spring/Summer 2021.

No abstract

In order to assess the reliability of a complex industrial system by simulation, and in reasonable time, variance reduction methods such as importance sampling can be used. We propose an adaptation of this method for a class of multi-component dynamical systems which are modeled by piecewise deterministic Markovian processes (PDMP). We show how to adapt the importance sampling method to PDMP, by introducing a reference measure on the trajectory space. This reference measure makes it possible to identify the admissible importance processes. Then we derive the characteristics of an optimal importance process, and present a convenient and explicit way to build an importance process based on theses characteristics. A simulation study compares our importance sampling method to the crude Monte-Carlo method on a three-component systems. The variance reduction obtained in the simulation study is quite spectacular.1991 Mathematics Subject Classification. 60K10;90B25;62N05.The dates will be set by the publisher. A model based on a PDMPDue to the complexity of the systems the reliability analysis is often done through an event tree analysis [4] which requires static approximations of the system, and relies on conservative approximations. With the development of computational capacities, it is now possible to consider more accurate tools for reliability

The assessment of the probability of a rare event with a naive Monte Carlo method is computationally intensive, so faster estimation or variance reduction methods are needed. We focus on one of these methods which is the interacting particle system (IPS) method. The method is not intrusive in the sense that the random Markov system under consideration is simulated with its original distribution, but selection steps are introduced that favor trajectories (particles) with high potential values. An unbiased estimator with reduced variance can then be proposed. The method requires to specify a set of potential functions. The choice of these functions is crucial because it determines the magnitude of the variance reduction. So far, little information was available on how to choose the potential functions. This paper provides the expressions of the optimal potential functions minimizing the asymptotic variance of the estimator of the IPS method and it proposes recommendations for the practical design of the potential functions.