Model Checking Interval Probabilistic Timed Automata
Interval probabilistic timed automata (IPTA) is put forward extending from probabilistic timed automata, and can be used to model network protocol or fault system with uncertain state transition probability. While we use PTCTL to denote the property of above systems, a solution to model check IPTA against PTCTL is presented. The key problems in the solution are calculating maximum probability and minimum probability on IPTA. To calculate maximum probability on IPTA, we first convert IPTA to interval Markov decision process with loose condition (LIMDP) through backward breath-first traverse based on symbolic state, and then give the strategy to calculate maximum probability on LIMDP. The calculation of minimum probability on IPTA can be converted to calculation of maximum probability on IPTA.
In this article we study monotone stochastic orders for real-valued processes with independent increments and derive sufficient deterministic conditions which are easy to verify and suitable for applications. Our proof is based on an explicit construction of a coupling. We also derive comparison results for L\'evy processes and semimartingales with conditionally independent increments.