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OMEGA Research team

Probabilistic numerical methods

  • Leader : Denis Talay
  • Research center(s) : CRI Sophia Antipolis - Méditerranée
  • Field : Numerical systems
  • Theme : Optimisation and inverse problems for stochastic or large-scale systems

Team presentation

The goal of this project, located both at INRIA Sophia Antipolis and INRIA Lorraine research units, is to develop and analyze probabilistic numerical methods such as Monte-Carlo and random vortex methods with an emphasis on two application fields: the partial differential equations of fluid mechanics or neutronics and the computing of complex quantities in financial mathematics.

Research themes

  • Simulation of the laws of stochastic processes, in particular discretization of stochastic differential equations.
  • Construction of appropriate probabilistic numerical methods from theoretical estimates on convergence rates, large deviation inequalities, and false convergence phenomena.
  • Implementation on parallel architectures.
  • The applications concern certain linear, or non-linear deterministic partial differential (or integro-differential) equations, systems with large numbers of interacting random particles, transport equations in neutronics, the development of money market or insurance problem models, the numerical computing of complex assets (exotic options, for example), the model risk analysis and the management of this risk for the hedging of options.

International and industrial relations

  • Partnership with EDF-Clamart, EDF-Chatou, CAR (Caisse des dépôts et consignations bank), the French Federation of insurance companies, Simulog, Risklab and SIP.
  • Joint research with Trento University (Italy), Purdue, California at Berkeley and North Carolina Universities (USA), Essex University (GB).
  • Coordination of the INRIA/NSF co-operation on the convergence in law of stochastic processes and numerical applications.
  • Within an European TTN, OMEGA works in partnership with SIP, FFSA and Simulog for the ProHPC-Finance project.

Keywords: Mathematical analysis Numerical analysis Approximation Stochastic process Stochastic differential equation Financial mathematics