@article{ConfortiKosenkovaRoelly2019,
  author    = {Conforti, Giovanni and Kosenkova, Tetiana and Roelly, Sylvie},
  title     = {Conditioned Point Processes with Application to Levy Bridges},
  series = {Journal of theoretical probability},
  volume    = {32},
  journal   = {Journal of theoretical probability},
  number    = {4},
  publisher = {Springer},
  address   = {New York},
  issn      = {0894-9840},
  doi       = {10.1007/s10959-018-0863-8},
  pages     = {2111 -- 2134},
  year      = {2019},
  abstract  = {Our first result concerns a characterization by means of a functional equation of Poisson point processes conditioned by the value of their first moment. It leads to a generalized version of Mecke's formula. En passant, it also allows us to gain quantitative results about stochastic domination for Poisson point processes under linear constraints. Since bridges of a pure jump L{\´e}vy process in Rd with a height a can be interpreted as a Poisson point process on space-time conditioned by pinning its first moment to a, our approach allows us to characterize bridges of L{\´e}vy processes by means of a functional equation. The latter result has two direct applications: First, we obtain a constructive and simple way to sample L{\´e}vy bridge dynamics; second, it allows us to estimate the number of jumps for such bridges. We finally show that our method remains valid for linearly perturbed L{\´e}vy processes like periodic Ornstein-Uhlenbeck processes driven by L{\´e}vy noise.},
  language  = {en}
}