Part I: Stochastic Hybrid Processes -- Toward a General Theory of Stochastic Hybrid Systems -- Hybrid Petri Nets with Diffusion that have Into-Mappings with Generalised Stochastic Hybrid Processes -- Part II: Analytical Approaches -- A Stochastic Approximation Method for Reachability Computations -- Critical Ovservability of a Class of Hybrid Systems and Application to Air Traffic Management -- Part III: Complexity and Randomization -- Monte Carlo Optimisation for Conflict Resolution in Air Traffic Control -- Branching and Interactign Particle Interpretations of Rare Event Probabilites.

Stochastic hybrid systems involve the coupling of discrete (logic based), continuous and probabilistic phenomena. Because of their versatility and generality, methods for modelling and analysis of stochastic hybrid systems have proved invaluable in a wide range of applications, including finance, air traffic control, biology, telecommunications, and embedded systems. Success stories in these application areas have made stochastic hybrid systems a very important, rapidly growing and dynamic research field since the beginning of the century, bridging the gap between stochastic analysis, computer science and control engineering. This volume presents a number of fundamental theoretical advances in the area of stochastic hybrid systems, motivated primarily from applications to air traffic management. Air traffic is arguably the most challenging application area for stochastic hybrid systems, since it requires handling complex distributed systems, multiple human in the loop elements and hybrid dynamics. The editors have collected key contributions, which define the state-of-the-art, present novel directions, and highlight emerging application areas.