Sandra Cerrai
University of Maryland
Department of Mathematics
College Park, MD 20742-4015
Math Building, room 2304
(301) 405 5460
Office Hours
Tu 3:30-4:30 and Th 12:30-1:30
Teaching
Spring 2009: Math 462
Fall 2009: Stat 400
Spring 2010: Stat 410, Math 462
Fall 2010: Stat 400, Stat 410
Spring 2011: Stat 600
Fall 2011: Stat 400, Stat 600
Spring 2012: Stat 601
My publications
Book
· Sandra Cerrai, Second order PDE's in finite and infinite dimensions. A probabilistic approach, x+330 pp. Lecture Notes in Mathematics 1762 (2001), Springer Verlag.
Articles
· Sandra Cerrai, Giuseppe Da Prato, Schauder estimates for elliptic equations in Banach spaces associated with stochastic reaction-diffusion equations, to appear in the Journal of Evolution Equations.
· Sandra Cerrai, Averaging principle for systems of RDEs with polynomial nonlinearities perturbed by multiplicative noise, to appear in the Siam Journal of Mathematical Analysis.
· Sandra Cerrai, Mark 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.
· Sandra Cerrai, Mark Freidlin, Approximation of quasi-potentials and exit problems for multidimensional RDE's with noise, Transactions of the AMS 363 (2011), pp. 3853-3892.
· Sandra Cerrai, Mark Freidlin, Fast transport asymptotics for stochastic RDE's with boundary noise, Annals of Probability 39 (2011), pp. 369-405.
· Sandra Cerrai, Normal deviations from the averaged motion for some reaction-diffusion equation with fast oscillating perturbation, Journal de Matematiques Pures et Appliques 91 (2009), pp. 614-647.
· Sandra Cerrai, A Khasminskii type averaging principle for stochastic reaction-diffusion equations, Annals of Applied Probability 19 (2009), pp. 899-948.
· Sandra Cerrai, Mark Freidlin, Averaging principle for a class of SPDE's, Probability Theory and Related Fields 144 (2009), pp. 137-177.
· Sandra Cerrai, Philippe Clement, Schauder estimates for a degenerate second order elliptic operator on a cube, Journal of Differential Equations 242 (2007), pp. 287-321.
· Sandra Cerrai, Mark Freidlin, Smoluchowski-Kramers approximation for a general class of SPDE's, Journal of Evolution Equations 6 (2006), pp. 657-689.
· Sandra Cerrai, Mark 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.
· Sandra Cerrai, Stabilization by noise for a class of stochastic reaction-diffusion equations, Probability Theory and Related Fields 133 (2005), pp. 190-214
· Sandra Cerrai, Philippe Clement, Erratum to "Schauder estimates for a class of second order elliptic operators on a cube", Bulletin des Sciences Mathematiques 129 (2005), p. 368.
· Sandra Cerrai, Michael Roeckner, Large deviations for invariant measures of stochastic reaction-diffusion systems with multiplicative noise and non-Lipschitz reaction term, Annales de l'Institut Henri Poincare (Probabilites et Statistiques) 41 (2005), pp. 69-105.
· Sandra Cerrai, Philippe Clement, Well-posedness of the martingale problem for some degenerate diffusion processes occurring in dynamics of populations, Bulletin des Sciences Mathematiques 128 (2004), pp. 355-389.
· Sandra Cerrai, Michael Roeckner, Large deviations for stochastic reaction-diffusion systems with multiplicative noise and non-Lipschitz reaction term, Annals of Probability 32 (2004), pp. 1-40.
· Sandra Cerrai, Michael Roeckner, Large deviations for invariant measures of general stochastic reaction-diffusion systems, Comptes Rendus Acad. Sci. Paris S. I Math. 337 (2003), pp. 597-602.
· Sandra Cerrai, Stochastic reaction-diffusion systems with multiplicative noise and non-Lipschitz reaction term, Probability Theory and Related Fields 125 (2003), pp. 271-304.
· Sandra Cerrai, Philippe Clement, Schauder estimates for a class of second order elliptic operators on a cube, Bulletin des Sciences Mathematiques 217 (2003), pp. 669-688.
· Sandra Cerrai, Philippe Clement, 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 Optimizatio 40 (2001), pp. 824-852.
· Sandra Cerrai, Optimal control problems for stochastic reaction-diffusion systems with non Lipschitz coefficients, SIAM Journal on Control and Optimization 39 (2001), pp. 1779-1816.
· Sandra Cerrai, Analytic semigroups and degenerate elliptic operators with unbounded coefficients: a probabilistic approach, Journal of Differential Equations 166 (2000), pp. 151-174.
· Sandra Cerrai, Ergodicity for stochastic reaction-diffusion systems with polynomial coefficients, Stochastics and Stochastics Reports 67 (1999), pp. 17-51.
· Sandra Cerrai, Differentiability of Markov semigroup for stochastic reaction-diffusion equations and applications to control, Stochastic Processes and their Applications 83 (1999) pp.15-37.
· Sandra Cerrai, Smoothing properties of transition semigroups relative to SDEs with value in Banach spaces, Probability Theory and Related Fields 113 (1999) pp. 85-114.
· Sandra Cerrai, Kolmogorov equations in Hilbert spaces with non smooth coefficients, Communications in Applied Analysis 2 (1998) pp. 271-298.
· Sandra Cerrai, Differentiability with respect to initial datum for solutions of SPDE's with no Fr\'{e}chet differentiable drift term, Communications in Applied Analysis 2 (1998) pp. 249-270
· Sandra Cerrai, Some results for second order elliptic operators having unbounded coefficients, Differential and Integral Equations 11 (1998) pp. 561-588.
· Sandra Cerrai, Invariant measures for a class of SDE's with drift term having polynomial growth, Dynamic Systems and Applications 5 (1996), 353-370.
· Sandra Cerrai, Elliptic and parabolic equations in R^n with coefficients having polynomial growth, Communications in Partial Differential Equations 21 (1996) 281-317.
· Sandra Cerrai, Fausto Gozzi, Strong solutions of Cauchy problems associated to weakly continuous semigroups, Differential and Integral Equations 8 (1995) 465-486.
· Sandra Cerrai, Weakly continuous semigroups in the space of functions with polynomial growth, Dynamic Systems and Applications 4 (1995) 351-372.
· Sandra Cerrai, A Hille Yosida theorem for weakly continuous semigroups , Semigroup Forum 49 (1994) 349-367.
Articles in volumes (refereed)
· Sandra Cerrai, Ergodic properties of reaction-diffusion equations perturbed by a degenerate multiplicative noise, Operator Theory: Advances and Applications vol. 168 (2006), Birkhauser Verlag Basel, pp. 45-59.
· Sandra Cerrai, Asymptotic behavior of systems of SPDE's 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.
· Sandra Cerrai, Classical solutions for Kolmogorov equations in Hilbert spaces, Third Seminar on Stochastic Analysis, Random Fields and Applications, Ascona, Progress in Probability 52, Birkhuser Verlag, (2002), pp. 55-72
· Sandra Cerrai, A generalization of the Bismut-Elworthy formula, Evolution Equations and their Applications in Physical and Life Sciences, edited by G. Lumer and L. Wiess, Lecture Notes in Pure and Applied Mathematics Vol. 215, Marcel Dekker (2000).