Publications

S. Cerrai, Second order PDEs in finite and infinite dimensions. A probabilistic approach, Lecture Notes in Mathematics 1762 (2001), Springer Verlag.

S. Cerrai, G. Guatteri, G. Tessitore, Nonlinear random perturbations of reaction-diffusion equations, arXiv:2506.17094

S. Cerrai, M. Xie,  Parabolic scaling of a stochastic wave map with co-normal noise: limit and fluctuations, arXiv:2506.06520

S. Cerrai, W. Hsu, SPDEs on narrow channels and graphs: convergence and large deviations in case of non-smooth noise, arXiv:2403.13493

S. Cerrai, A. Debussche, Smoluchowski-Kramers diffusion approximation for systems of stochastic damped wave equations with non-constant friction, arXiv:2312.08925

Z. Brzezniak, S. Cerrai, Stochastic wave equations with constraints: well-posedness and Smoluchowski-Kramers diffusion approximation, Communications in Mathematical Physics, 406 (2025), paper n. 223, pp. 1--59.

S. Cerrai, A. Lunardi, Smoothing effects and maximal Hölder regularity for non-autonomous Kolmogorov equations in infinite dimension, Journal of Differential Equations, 434 (2025), pp. 1-40.

S. Cerrai, Y. Zhu, Averaging principle for slow-fast systems of stochastic PDEs with rough coefficients, Stochastic Processes and Their Applications, 183 (2025), pp. 1-27.

S. Cerrai, M. Xie, The small-mass limit for some constrained wave equations with nonlinear conservative noise, Electronic Journal of Probability, 30 (2025) paper no. 25, pp. 1-27

S. Cerrai. M. Xie, On the small-mass limit for stationary solutions of stochastic wave equations with state-dependent friction, Applied Mathematics, and Optimization, 90 (2024), paper n. 7, 48 pp.

S. Cerrai, G. Guatteri, G. Tessitore, Nonlinear random perturbations of PDEs and quasi-linear equations in Hilbert spaces depending on a small parameter, Journal of Functional Analysis, 286 (2024), pp. 1--57

S. Cerrai, M. Xie, On the small noise limit in the Smoluchowski-Kramers approximation of nonlinear wave equations with variable friction, Transactions of the American Mathematical Society, 372 (2023), pp. 7651--7689

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. 1651-1681

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

S. Cerrai, G. Xi, Incompressible viscous fluids in R^2 and SPDEs on graphs, in the presence of fast advection and nonsmooth noise, Annales de L'Institut Henri Poincaré - Probabilités et Statistiques 57 (2021), pp. 1636-1664

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

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

S. Cerrai, A. Lunardi, Schauder theorems for Ornstein-Uhlenbeck equations in infinite dimension, Journal of Differential Equations 267 (2019), pp. 7462–7482

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

S. Cerrai, A. Debussche, Large deviations for the dynamic Phi^{2n}_d model, Applied Mathematics and Optimization 80 (2019), pp. 81–102

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

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.

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.

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.

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.

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. 

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. 

S. Cerrai, M. Salins, Smoluchowski-Kramers approximation and large deviations for infinite dimensional non-gradient systems with applications to the exit problem, Annals of Probability 44 (2016), pp. 2591–2642. 

S. Cerrai, M. Freidlin, Large deviations for the Langevin equation with strong damping, Journal of Statistical Physics 161 (2015), pp. 859–875. 

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. 

S. Cerrai, M. Salins, Smoluchowski-Kramers approximation and large deviations for infinite dimensional gradient systems, Asymptotics Analysis 88 (2014), pp. 201-215. 

S. Cerrai, G. Da Prato, A basic identity for Kolmogorov operators in the space of continuous functions related to RDEs with multiplicative noise, Annals of Probability 42 (2014), pp. 1297-1336. 

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. 

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. 

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. 

S. Cerrai, M. Freidlin, Small mass asymptotics for a charged particle in a magnetic field and long-time influence of small perturbations, Journal of Statistical Physics 144 (2011), pp. 101-123. 

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. 

S. Cerrai, M. Freidlin, Fast transport asymptotics for stochastic RDE’s with boundary noise, Annals of Probability 39 (2011), pp. 369-405. 

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.

S. Cerrai, A Khasminskii type averaging principle for stochastic reaction-diffusion equations, Annals of Applied Probability 19 (2009), pp. 899-948.

S. Cerrai, M. Freidlin, Averaging principle for a class of SPDEs, Probability Theory and Related Fields 144 (2009), pp. 137-177. 

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. 

S. Cerrai, M. Freidlin, Smoluchowski-Kramers approximation for a general class of SPDEs, Journal of Evolution Equations 6 (2006), pp. 657-689. 

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. 

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. 

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. 

S. Cerrai, Stabilization by noise for a class of stochastic reaction-diffusion equations, Probability Theory and Related Fields 133 (2005), pp. 190-214. 

S. Cerrai, P. Clément, Corrigendum to ”Schauder estimates for a class of second order elliptic operators on a cube”, Bulletin des Sciences Mathématiques 129 (2005), p. 368. 

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. 

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.
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. 

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. 

S. Cerrai, Stochastic reaction-diffusion systems with multiplicative noise and non- Lipschitz reaction term, Probability Theory and Related Fields 125 (2003), pp. 271-304. 

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. 

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. 

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. 

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. 

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. 

S. Cerrai, Analytic semigroups and degenerate elliptic operators with unbounded coefficients: a probabilistic approach, Journal of Differential Equations 166 (2000), pp. 151-174. 

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).  

S. Cerrai, Ergodicity for stochastic reaction-diffusion systems with polynomial coefficients, Stochastics and Stochastics Reports 67 (1999), pp. 17-51. 

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.

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. 

S. Cerrai, Kolmogorov equations in Hilbert spaces with non-smooth coefficients, Communications in Applied Analysis 2 (1998) pp. 271-298. 

S. Cerrai, Differentiability with respect to initial datum for solutions of SPDEs with no Fréchet differentiable drift term, Communications in Applied Analysis 2 (1998) pp. 249- 270. 

S. Cerrai, Some results for second order elliptic operators having unbounded coefficients, Differential and Integral Equations 11 (1998) pp. 561-588.

S. Cerrai, Invariant measures for a class of SDEs with drift term having polynomial growth, Dynamic Systems and Applications 5 (1996), pp. 353-370. 

S. Cerrai, Elliptic and parabolic equations in R^n with coefficients having polynomial growth, Communications in Partial Differential Equations 21 (1996) pp. 281-317.

S. Cerrai, F. Gozzi, Strong solutions of Cauchy problems associated to weakly continuous semigroups, Differential and Integral Equations 8 (1995) pp. 465-486. 

S. Cerrai, Weakly continuous semigroups in the space of functions with polynomial growth, Dynamic Systems and Applications 4 (1995) pp. 351-372.

S. Cerrai, A Hille Yosida theorem for weakly continuous semigroups, Semigroup Forum 49 (1994) pp. 349-367.