@PhdThesis{julien2026,
  author   = {Julien, David},
  school   = {Nantes Université},
  title    = {Probabilistic Abstraction and Verification of Hybrid Dynamical Systems},
  year     = {2026},
  month    = dec,
  type     = {phdthesis},
  abstract = {This thesis presents the formal verification of systems described with ordinary differential equations. Two main results may be distinguished. First, the adaptation of Statistical Model Checking (SMC) to the context of differential equations, by bounding the error introduced by integrations methods for the resolution of these equations on the whole simulation space. Second, the abstraction of socalled hybrid systems, whose dynamics is described by a differential equations which can be modified during the simulation, as a Markov process: this allows to overcome some limitations imposed by the original formalism. Each of the two presented techniques is completely unfolded on a case study.},
  doi      = {10.70675/c48944d0z9a37z4f92zbb01z93e71ee1a530},
  keywords = {Ordinary Differential Equations,Simulation,Markov Processes},
  url      = {https://theses.hal.science/tel-05802690},
}