Dynamical systems and probability. Quantitative finance

Research team

  • Giulia Livieri
    Researcher
  • Dejun Luo
    Fellow
  • Paolo Giulietti
    Fellow
  • Francesco Grotto
    PhD Student
  • Anastasia Shepelevtseva
    PhD Student
  • Francesco Cordoni
    PhD Student
  • Maddalena Ghio
    PhD Student
  • Matteo Ottaviani
    PhD Student
  • Alessio Brini
    PhD Student
  • Iacopo Raffaelli
    PhD Student

Research themes in Probability

  • Stochastic partial differential equations
  • Systems of interacting particles
  • Limits of scale
  • Applications in climate sciences

Miur PRIN 2015, title "Deterministic and stochastic evolution equations" Progetto biennale SNS

Activities

Participation at a conference at the CIRM in Luminy, at the Hausdorff Center in Bonn, at the Accademia dei Lincei in Rome. Seminars at ETH Zurich and University of Delft.

Held mini-courses for a Winter School at the University of Bologna and for a semester on climate sciences at the Institute Henri Poincaré in Paris.

Organizer of a Winter School in Augsburg, a conference in Cortona and a conference in Vietri.

“LEANING TORI” dynamical systems , An Hamiltonian Event under the Tower workshop at Centro De Giorgi

DinAmici IV workshop at the Centro De Giorgi

Summer School for Economic and Social Sciences: San Miniato, settembre 2019

Publications

  • Franco Flandoli, Dejun Luo, Point vortex approximation for 2D Navier--Stokes equations driven by space-time white noise , arXiv:1902.09338.
  • Franco Flandoli, Renormalized Onsager functions and merging of vortex clusters , arXiv:1902.06565
  • Franco Flandoli, Marta Leocata, Cristiano Ricci, The Navier-Stokes-Vlasov-Fokker-Planck system as a scaling limit of particles in a fluid, arXiv:1811.07924.
  • Giuseppe Da Prato, Franco Flandoli, Michael Reockner, Continuity equation in LlogL for the 2D Euler equations under the enstrophy measure, to appear on SPDE.
  • Franco Flandoli, Dejun Luo, Convergence of transport noise to Ornstein-Uhlenbeck for 2D Euler equations under the enstrophy measure, arXiv:1806.09332, to appear on Ann. Probab.
  • Franco Flandoli, Dejun Luo, Energy conditional measures and 2D turbulence, JOURNAL MATH. PHYS. 61 (2020), no. 1, 013101, 22 pp.
  • Lisa Beck, Franco Flandoli, Massimiliano Gubinelli, M ario Maurelli , Stochastic ODEs and stochastic linear PDEs with critical drift: regularity, duality and uniqueness. ELECTRONIC J. PROBAB. 24 (2019), Paper No. 136, 72 pp.
  • Franco Flandoli, Marta Leocata, A particle system approach to aggregation phenomena, JOURNAL APPL. PROBAB. 56 (2019), no. 1, 282–306.
  • Franco Flandoli, Martin Saal, mSQG equations in distributional spaces and point vortex approximation, JOURNAL EVOL. EQU. 19 (2019), no. 4, 1071–1090.
  • Franco Flandoli, Marta Leocata, Cristiano Ricci, The Vlasov-Navier-Stokes equations as a mean field limit, DISCRETE CONTIN. DYN. SYST. 24 (2019), no. 8, 3741–3753. Paolo Buttà,
  • Franco Flandoli, Michela Ottobre, Bogusław Zegarliński, A non-linear kinetic model of self-propelled particles with multiple equilibria, KINETIC RELATED MODELS 12 (2019), no. 4, 791–827.
  • Franco Flandoli, Dejun Luo, Kolmogorov equations associated to the stochastic 2D Euler equations, SIAM J. MATH. ANAL. 51 (2019), no. 3, 1761–1791.
  • Franco Flandoli, Dejun Luo, Euler-Lagrangian approach to 3D stochastic Euler equations, JOURNAL GEOM. MECH. 11 (2019), no. 2, 153–165. Hakima Bessaih , Michele Coghi ,
  • Franco Flandoli, Mean field limit of interacting filaments for 3D Euler equations, JOURNAL STAT. PHYS. 174 (2019), no. 3, 562–578.
  • Franco Flandoli, Dejun Luo, ρ-white noise solution to 2D stochastic Euler equations, PROBAB. THEORY RELATED FIELDS, 175 (2019), no. 3-4, 783–832.
  • Franco Flandoli, Enrico Priola, Giovanni Zanco, A mean-field model with discontinuous coefficients for neurons with spatial interaction, DISCRETE CONTIN. DYN. SYST. 39 (2019), no. 6, 3037–3067.
  • Vincenzo Capasso, Franco Flandoli, On the mean field approximation of a stochastic model of tumor-induced angiogenesis, EUROPEAN J. APPL. MATH. 30 (2019), no. 4, 619–658.