Publications


Book

  • S. Cerrai, Second order PDE’s in finite and infinite dimensions. A probabilistic approach, x+330 pp. Lecture Notes in Mathematics 1762 (2001), Springer Verlag. PDF


Articles

  • Z. Brzezniak, S. Cerrai, Stochastic wave equations with constraints: well-posedness and Smoluchowski-Kramers diffusion approximation, arXiv: 2303.09717, PDF
  • S. Cerrai, Y. Zhu, Averaging principle for slow-fast systems of stochastic PDEs with rough coefficients, arXiv: 2212.14552, PDF
  • S. Cerrai, G. Guatteri, G. Tessitore, Nonlinear random perturbations of PDEs and quasi-linear equations in Hilbert spaces depending on a small parameter, arXiv: 2208.12867, PDF
  • S. Cerrai, M. Xie, On the small noise limit in the Smoluchowski-Kramers approximation of nonlinear wave equations with variable friction, arXiv: 2203.05923, PDF
  • S. Cerrai, A. Lunardi, Smoothing effects and maximal Hölder regularity for non-autonomous Kolmogorov equations in infinite dimension, arXiv: 2111.05421, PDF
  • S. Cerrai, N. Paskal, Large deviations for the invariant measures of the 2D stochastic Navier-Stokes equation with vanishing noise correlation, Stochastic and Partial Differential Equations: Analysis and Computations 10 (2022), pp. 16511681, PDF
  • S. Cerrai, G. Xi, A Smoluchowski-Kramers approximation for an infinite dimensional system with state-dependent damping, Annals of Probability 50 (2022), pp. 874-904, PDF
  • S. Cerrai, G. Xi, Incompressible viscous fluids in R^2 and SPDEs on graphs, in  presence of fast advection and non smooth noise, Annales de l'Institut Henri Poincaré - Probabilités et Statistiques 57 (2021), pp. 1636-1664, PDF
  • S. Cerrai, J. Wehr, Y. Zhu, An averaging approach to the Smoluchowski-Kramers approximation in the presence of a varying magnetic field, Journal of Statistical Physics 181 (2020), pp. 132–148, PDF
  • S. Cerrai, N. Glatt-Holtz, On the convergence of stationary solutions in the Smoluchowski-Kramers approximation of infinite dimensional systems, Journal of Functional Analysis 278 (2020), pp. 1-38 PDF
  • S. Cerrai, A. Lunardi, Schauder theorems for Ornstein-Uhlenbeck equations in infinite dimension, Journal of Differential Equations 267 (2019), pp. 7462–7482. PDF
  • S. Cerrai, N. Paskal, Large deviations for fast transport stochastic RDEs with applications to the exit problem, Annals of Applied Probability 29 (2019), pp. 1993-2032. PDF
  • S. Cerrai, A. Debussche, Large deviations for the dynamic Phi^{2n}_d model, Applied Mathematics and Optimization 80 (2019), pp. 81–102. PDF
  • S. Cerrai, M. Freidlin: Fast flow asymptotics for stochastic incompressible viscous fluids in R^2 and SPDEs on graphs, Probability Theory and Related Fields 173 (2019), pp. 491–535. PDF
  • S. Cerrai, A. Debussche, Large deviations for the two-dimensional stochastic Navier-Stokes equation with vanishing noise correlation, Annales de l’Institut Henri Poincaré 55 (2019), pp. 211-236. PDF
  • S. Cerrai, A. Lunardi, Averaging principle for non autonomous slow-fast systems of stochastic RDEs: the almost periodic case, Siam Journal of Mathematical Analysis 49 (2017), pp. 2843-2884. PDF
  • Z. Brzézniak, S. Cerrai, Large deviation principle for the invariant measures of the 2D stochastic Navier-Stokes equations on a torus, Journal of Functional Analysis 273 (2017) pp. 1891-1930. PDF
  • S. Cerrai, M. Freidlin, SPDEs on narrow domains and on graphs: an asymptotic approach, Annales de l’Institut Henri Poincaré 53 (2017) pp. 865–899. PDF
  • S. Cerrai, M. Salins, On the Smoluchowski-Kramers approximation for a system with an infinite number of degrees of freedom subject to a magnetic field, Stochastic Processes and Their Applications 127 (2017) pp. 273–303. PDF
  • S. Cerrai, M. Freidlin, M. Salins, On the Smoluchowski-Kramers approximation for SPDEs and its interplay with large deviations and long time behavior, Discrete and Continuous Dynamical Systems, Series A, 37 (2017), pp. 33–76. PDF
  • S. Cerrai, M. Salins, Smoluchowski-Kramers approximation and large deviations for infinite dimensional non-gradient systems with applications to the exit problem, The Annals of Probability 44 (2016), pp. 2591–2642. PDF
  • S. Cerrai, M. Freidlin, Large deviations for the Langevin equation with strong damping, Journal of Statistical Physics 161 (2015), pp. 859–875. PDF
  • Z. Brzézniak, S. Cerrai, M. Freidlin, Quasipotential and exit times for 2D Stochastic Navier-Stokes equations driven by space-time white noise, Probability Theory and Related Fields 162 (2015), pp. 739–793. PDF
  • S. Cerrai, M. Salins, Smoluchowski-Kramers approximation and large devia- tions for infinite dimensional gradient systems, Asymptotics Analysis 88 (2014), pp. 201-215. PDF
  • S. Cerrai, G. Da Prato, A basic identity for Kolmogorov operators in the space of continuous functions related to RDEs with multiplicative noise, The Annals of Probability 42 (2014), pp. 1297-1336. PDF
  • S. Cerrai, G. Da Prato, F. Flandoli, Pathwise uniqueness for stochastic reaction-diffusion equations in Banach spaces with an Hölder drift component, Stochastic Partial Differential Equations: Analysis and Computations 1 (2013), pp. 507- 551. PDF
  • S. Cerrai, G. Da Prato, Schauder estimates for elliptic equations in Banach spaces associated with stochastic reaction-diffusion equations, Journal of Evolution Equations 12 (2012), pp. 83-98. PDF
  • S. Cerrai, Averaging principle for systems of RDEs with polynomial nonlinearities perturbed by multiplicative noise, Siam Journal of Mathematical Analysis 43 (2011), pp. 2482- 2518. PDF
  • S. Cerrai, M. Freidlin, Small mass asymptotics for a charged particle in magnetic field and long-time influence of small perturbations, Journal of Statistical Physics 144 (2011), pp. 101-123. PDF
  • S. Cerrai, M. Freidlin, Approximation of quasi-potentials and exit problems for multidimensional RDE’s with noise, Transactions of the AMS 363 (2011), pp. 3853-3892. PDF
  • S. Cerrai, M. Freidlin, Fast transport asymptotics for stochastic RDE’s with boundary noise, Annals of Probability 39 (2011), pp. 369-405. PDF
  • S. Cerrai, Normal deviations from the averaged motion for some reaction-diffusion equation with fast oscillating perturbation, Journal de Matématiques Pures et Appliqués 91 (2009), pp. 614-647. PDF
  • S. Cerrai, A Khasminskii type averaging principle for stochastic reaction-diffusion equations, Annals of Applied Probability 19 (2009), pp. 899-948. PDF
  • S. Cerrai, M. Freidlin, Averaging principle for a class of SPDEs, Probability Theory and Related Fields 144 (2009), pp. 137-177. PDF
  • S. Cerrai, P. Clément, Schauder estimates for a degenerate second order elliptic operator on a cube, Journal of Differential Equations 242 (2007), pp. 287-321. PDF
  • S. Cerrai, M. Freidlin, Smoluchowski-Kramers approximation for a general class of SPDEs, Journal of Evolution Equations 6 (2006), pp. 657-689. PDF
  • S. Cerrai, M. Freidlin, On the Smoluchowski-Kramers approximation for a system with an infinite number of degrees of freedom, Probability Theory and Related Fields 135 (2006), pp. 363-394. PDF
  • S. Cerrai, Ergodic properties of reaction-diffusion equations perturbed by a degenerate multiplicative noise, Operator Theory: Advances and Applications vol. 168 (2006), Birkhäuser Verlag Basel, pp. 45-59. PDF
  • S. Cerrai, Asymptotic behavior of systems of SPDEs with multiplicative noise, Stochastic Partial Differential Equations and Applications VII, Lecture Notes in Pure and Applied Mathematics vol. 245 (2006), Chapman and Hall/CRC Press, pp. 61-75. PDF
  • S. Cerrai, Stabilization by noise for a class of stochastic reaction-diffusion equations, Probability Theory and Related Fields 133 (2005), pp. 190-214. PDF
  • S. Cerrai, P. Clément, Erratum to ”Schauder estimates for a class of second order elliptic operators on a cube”, Bulletin des Sciences Mathématiques 129 (2005), p. 368. PDF
  • S. Cerrai, M. Röckner, Large deviations for invariant measures of stochastic reaction-diffusion systems with multiplicative noise and non-Lipschitz reaction term, Annales de l’Institut Henri Poincaré (Probabilités et Statistiques) 41 (2005), pp. 69-105. PDF
  • S. Cerrai, P. Clément, Well-posedness of the martingale problem for some degenerate diffusion processes occurring in dynamics of populations, Bulletin des Sciences Mathématiques 128 (2004), pp. 355-389. PDF
    S. Cerrai, M. Röckner,     Large deviations for stochastic reaction-diffusion systems with multiplicative noise and non-Lipschitz reaction term, Annals of Probability 32 (2004), pp. 1-40. PDF
  • S. Cerrai, M. Röckner, Large deviations for invariant measures of general stochastic reaction-diffusion systems, Comptes Rendus Acad. Sci. Paris S. I Math. 337 (2003), pp. 597-602. PDF
  • S. Cerrai, Stochastic reaction-diffusion systems with multiplicative noise and non- Lipschitz reaction term, Probability Theory and Related Fields 125 (2003), pp. 271-304. PDF
  • S. Cerrai, P. Clément, Schauder estimates for a class of second order elliptic operators on a cube, Bulletin des Sciences Mathématiques 217 (2003), pp. 669-688. PDF
  • S. Cerrai, Classical solutions for Kolmogorov equations in Hilbert spaces, Third Seminar on Stochastic Analysis, Random Fields and Applications, Ascona, Progress in Probability 52, Birkhäuser Verlag, (2002), pp. 55-72. PDF
  • S. Cerrai, P. Clément, On a class of degenerate elliptic operators arising from the Fleming-Viot processes, Journal of Evolution Equations 1 (2001), pp. 243-276. PDF
  • Sandra Cerrai, Stationary Hamilton-Jacobi equations in Hilbert spaces and applications to a stochastic optimal control problem, SIAM Journal on Control and Optimization 40 (2001), pp. 824-852. PDF
  • S. Cerrai, Optimal control problems for stochastic reaction-diffusion systems with non Lipschitz coefficients, SIAM Journal on Control and Optimization 39 (2001), pp. 1779-1816. PDF
  • S. Cerrai, Analytic semigroups and degenerate elliptic operators with unbounded coefficients: a probabilistic approach, Journal of Differential Equations 166 (2000), pp. 151-174. PDF
  • S. Cerrai, A generalization of the Bismut-Elworthy formula, Evolution Equations and their Applications in Physical and Life Sciences, Lecture Notes in Pure and Applied Mathematics Vol. 215, Marcel Dekker (2000).  PDF
  • S. Cerrai, Ergodicity for stochastic reaction-diffusion systems with polynomial coefficients, Stochastics and Stochastics Reports 67 (1999), pp. 17-51. PDF
  • S. Cerrai, Differentiability of Markov semigroup for stochastic reaction-diffusion equations and applications to control, Stochastic Processes and their Applications 83 (1999) pp.15-37. PDF
  • S. Cerrai, Smoothing properties of transition semigroups relative to SDEs with value in Banach spaces, Probability Theory and Related Fields 113 (1999) pp. 85-114. PDF
  • S. Cerrai, Kolmogorov equations in Hilbert spaces with non smooth coefficients, Com- munications in Applied Analysis 2 (1998) pp. 271-298. PDF
  • S. Cerrai, Differentiability with respect to initial datum for solutions of SPDE’s with no Fréchet differentiable drift term, Communications in Applied Analysis 2 (1998) pp. 249- 270. PDF
  • S. Cerrai, Some results for second order elliptic operators having unbounded coefficients, Differential and Integral Equations 11 (1998) pp. 561-588. PDF
  • S. Cerrai, Invariant measures for a class of SDEs with drift term having polynomial growth, Dynamic Systems and Applications 5 (1996), 353-370. PDF
  • S. Cerrai, Elliptic and parabolic equations in Rn with coefficients having polynomial growth, Communications in Partial Differential Equations 21 (1996) 281-317. PDF
  • S. Cerrai, F. Gozzi, Strong solutions of Cauchy problems associated to weakly continuous semigroups, Differential and Integral Equations 8 (1995) 465-486. PDF
  • S. Cerrai, Weakly continuous semigroups in the space of functions with polynomial growth, Dynamic Systems and Applications 4 (1995) 351-372. PDF
  • S. Cerrai, A Hille Yosida theorem for weakly continuous semigroups, Semigroup Forum 49 (1994) 349-367. PDF



© Sandra Cerrai 2017