|Stochastic models are important when dealing with system affected by an uncertainty. They allow for a range of application areas, a few examples being Biology, Power Networks and Finance.
This project is focused on the analysis and control synthesis performed over complex stochastic models, in particular Markov processes and Stochastic Hybrid Systems. We use the tools of Applied Mathematics and Computer Science to come up with novel approaches to the problem, formal on the one hand and computationally efficient on the other. A special attention is paid to such methods as model-checking and approximate bisimulation: non-classical optimal control techniques that have quickly showed their advantages.
The outcomes of our research on a theoretical side are further tested on the benchmark examples in Finance (ruin of an insurance company, default cascades in financial networks) and Biology (control of a protein expression in a cell).