Reach Probability Estimation of Rare Events in Stochastic Hybrid Systems

This thesis conducts a series of interrelated research studies on reach probability estimation of rare events for stochastic hybrid systems. Chapter 1 explains that the motivation for these studies stems from the need to assess safety and capacity of a design for a future Air Traffic Management (ATM) concept of operations (ConOps). The safety...

Interacting Particle System based estimation of reach probability of General Stochastic Hybrid Systems

For diffusions, a well-developed approach in rare event estimation is to introduce a suitable factorization of the reach probability and then to estimate these factors through simulation of an Interacting Particle System (IPS). This paper studies IPS based reach probability estimation for General Stochastic Hybrid Systems (GSHS). The...

Interacting Particle System-based Estimation of Reach Probability for a Generalized Stochastic Hybrid System

This paper studies estimation of reach probability for a generalized stochastic hybrid system (GSHS). For diffusion processes a well-developed approach in reach probability estimation is to introduce a suitable factorization of the reach probability and then to estimate these factors through simulation of an Interacting Particle System (IPS)....

Verification of Cascading Events in Interconnected Stochastic Systems: Using Adaptive Parametric Importance Sampling Methods

Verification of rare cascading events in interconnected Markov processes are of high interest in energy grids, computer networks, and banking systems. Small defaults may lead to a global cascade of failures in the network. In this work, the rare events of contagious bankruptcies of the interconnected banking system are verified by three adaptive...

Adaptive and Sequential Gridding Procedures for the Abstraction and Verification of Stochastic Processes

This work is concerned with the generation of finite abstractions of general state-space processes to be employed in the formal verification of probabilistic properties by means of automatic techniques such as probabilistic model checkers. The work employs an abstraction procedure based on the partitioning of the state-space, which generates a...

On strong Markov property of solutions to stochastic differential equations on hybrid state spaces

In this paper we study a class of strong Markov solutions to stochastic differential equations on a hybrid state spaces. We construct stochastic hybrid processes as solutions to Ito-Skorohod type stochastic differential equations. Then we present strong existence and uniqueness results and show that under weak conditions these solutions are...