Probability and Mathematical Statistics

Research interests

  • Stochastic processes connected to risk theory and to stochastic modelling in finance. Large deviations, with applications to simulation and to numerical methods in risk theory and finance; ruin probabilities for complex models and variance reduction for their computation by simulation, in particular for long memory or heavy tail models; Monte Carlo methods for the pricing/hedging of options via Malliavin calculus techniques.
  • Isotropic random fields. Characterizations, harmonic analysis, connections with representation theory, high frequency asymptotics.
  • Stochastic modelling and statistics in biology and medicine. First passage times and inverse problems. Methods and models in medical statistics. Modelling and statistics of disease spread.
  • Filtering. Filtering with delayed data; non linear filtering and applications to partially observed queues model estimation; high frequency data models and estimates.
  • Statistical inference on stochastic processes and random fields. Spectral analysis of stationary and nonstationary processes, long memory, cointegration and fractional cointegration; statistics of spherical random fields, higher order angular power spectra, spherical wavelets, application to cosmological data.
  • Random processes on random structures. Random walks in random environment, spatial random graphs, particle systems and hydrodynamic limits, stochastic homogenization, mixing time.
  • Statistical learning. Neural networks, abstract and applied harmonic analysis, wavelet transform, coorbit space theory, frame theory.