Annie Millet

Annie Millet Version française

Professor at the University Paris 1 Panthéon Sorbonne
Equipe SAMM (EA 4543)
email: millet
Phone: (+33 1) 44 07 88 60
Postal adress: SAMM, Université Paris 1, Centre Pierre Mendès France,
90 rue de Tolbiac, F- 75634 Paris Cedex 13.

and

LPMA, Research team Modélisation Stochastique
Phone: (+ 33 1) 57 27 92 72

I am in charge for Paris 1 of the Master M2MO Modélisation Aléatoire. Notes of my lectures on the Monte Carlo Method are available here Monte Carlo .

I am President of the Comité Consultatif Scientifique of sections 26-27 (Mathematics and Computer Sciences) in Paris 1, member of the Scientific Comitee of the University Paris 1 and of the parisian HDR Comitee in Mathematics .

Main research themes

Old research themes

Operator ergodic theory
Processes indexed by directed sets
Two-parameter processes
Optimal stopping and optimal control

Current research themes

Stochastic calculus and support theorems
Stochastic calculus of variations
Large deviations
Stochastic partial differential equations
Hydrodynamical models
Discretization schemes

Publications

The publications are gathered according to the main research themes. Notes aux Comptes Rendus announcing results published in forthcoming papers are not included in this list. The .pdf files of the most recent publications can be downloaded from this page or on arXiv.

Ergodic Theory

  1. Dilatations de certaines contractions de Lp, C.R. Acad. Paris, Série A t.283 (1976), p. 1041-1043. 2.
  2. Un théorème ergodique en moyenne, C.R. Acad. Sc. Paris, Série A t. 283 (1976),p. 1103-1106.
  3. On the existence of sigma-finite invariant measures for Lp-operators, Israel Journal of Mathematics 33 (1979), p. 349-367 (with L. Sucheston).
  4. Sur le théorème en moyenne d'Akcoglu-Sucheston, Mathematische Zeitschrift 172 (1980), p. 213-237.
  5. On fixed points and multiparameter ergodic theorems in Banach lattices, Canadian Journal of Mathematics 40 (1988), p. 429-458 (with L. Sucheston).

Processes Indexed by Directed Sets

  1. Sur la caractérisation des conditions de Vitali par la convergence essentielle des martingales, C.R. Acad. Sc. Paris, Série A t. 287 (1978), p. 887-890.
  2. Characterization of Vitali conditions with overlap in terms of convergence of classes of amarts, Canadian Journal of Mathematics 31 (1979), p. 1033-1046 (with L. Sucheston).
  3. La convergence essentielle des martingales bornées dans L1 n'implique pas la condition de Vitali V, C.R. Acad. Sc. Paris, Série A t. 288 (1979), p. 595-598 (with L. Sucheston).
  4. Convergence of classes of amarts indexed by directed sets - Characterization in terms of Vitali conditions, Canadian Journal of Mathematics 32 (1980) , p. 86-125 (with L. Sucheston).
  5. A characterization of Vitali conditions in terms of maximal inequalities, The Annals of Probability 8 (1980), p. 339-349 (with L. Sucheston).
  6. On convergence of L1-bounded martingales indexed by directed sets, Probability and Mathematical Statistics 1 (1980), p. 151-169 (with L. Sucheston).
  7. On covering conditions and convergence, Proceedings of the Conference on Measure Theory, Oberwolfach 1979, Lecture Notes in Mathematics 794 (1980), p. 431-454.

Two Parameter Processes

  1. Régularité à gauche des gauche des martingales fortes à plusieurs indices, C.R. Acad. Sc. Paris, Série A t.290 (1980), p. 773-776 (with J.P. Fouque).
  2. On regularity of multiparameter amarts and martingales, Zeitschrift für Wahrscheinlichkeitstheorie verwandte Gebiete 56 (1981), p. 21-45 (with L. Sucheston).
  3. On compactness and optimality of stopping times, Proceedings of the Conference on Martingale Theory in Harmonic Analysis and Banach Spaces, Lecture Notes in Mathematics 939 (1981), p. 36-61 (with G.A Edgar and L. Sucheston).
  4. Convergence and regularity of strong submartingales, Processus Aléatoires à deux Indices, Proceedings du Colloque E.N.S.T.- C.N.E.T. Paris 1980, Lecture Notes in Mathematics 863 (1981), p. 50-58.
  5. On convergence and regularity of (Delta 1) submartingales, Annales de l'Institut Henri Poincaré 19 (1983), p. 25-42.
  6. Demi-convergence of processes indexed by two indices, Annales de l'Institut Henri Poincaré 19 (1983), p. 175-187 (with L. Sucheston).

Optimal Control and Optimal Stopping

  1. On randomized tactics and optimal stopping in the plane, The Annals of Probability 13 (1985), p. 946-965.
  2. Points, lignes et systèmes d'arret flous et problème d'arret optimal, Seminaire de Probabilit\'es XX, Lecture Notes in Mathematics 1204 (1986), p. 81-94 (with G. Mazziotto).
  3. Stochastic control of two-parameter processes; application to the two-armed bandit problem, Stochastics 22 (1987), p. 251-288 (with G. Mazziotto).
  4. A probabilistic approach of the reduite, Probability and Mathematical Statistics 13 (1992), p. 97-121, (with N. El Karoui and J.P. Lepeltier).

Stochasic Calculus of Variations and Infinite Dimensional Analysis

  1. Integration by parts and time reversal for diffusion processes, The Annals of Probability 17 (1989),p. 208-238 (with D. Nualart and M. Sanz-Solé).
  2. Time reversal for infinite dimensional diffusions, Probability Theory and Related Fields 82 (1989), p. 315-347 (with D. Nualart and M. Sanz-Solé).
  3. Absolute Continuity of the law of an infinite-dimensional Wiener functional with respect to the Wiener probability, Probability Theory and Related Fields 85 (1990), p. 403-411 (with G. Mazziotto).
  4. An introduction to the stochastic calculus of variations and to the anticipative calculus, publication fom the Torun Univesity (1990).
  5. On the continuity of Ornstein-Uhlenbeck processes in infinite dimension, Probability Theory and Related fields 92 (1992), p. 529-547 (with W. Smolenski).
  6. Small perturbations of Gaussian regressors, Statistics and Probability Letters 24 (1995), p. 21-31 (with W. Smolenski).
  7. Points of positive density for the solution to a hyperbolic SPDE, Potential Analysis 7 (1997), p. 623-659 (with M. Sanz-Solé). Vous pouvez lire cet article en suivant le lien DOI
  8. Approximation of rough paths of fractional Brownian motion, Random Fields and Applications V Centro Stefano Franscini, Ascona, May 2005 Series: Progress in Probability, Vol. 59, p. 275-304 (2008), (with M. Sanz-Solé)

Large Deviations

  1. Small perturbations for quasilinear anticipating stochastic differential equations, International Series of Numerical Mathematics Birkhauser Verlag Basel Vol. 102 (1991), p. 149-157 (with D. Nualart and M. Sanz-Solé).
  2. Composition of large deviation principles and applications, Stochastic Analysis : Liber Amicorum for Moshe Zakai, Academic Press 1991, p. 383-396 (with D. Nualart and M. Sanz-Solé).
  3. Large deviations for a class of anticipating stochastic differential equations, The Annals of Probability 20 (1992), p. 1902-1931, (with D. Nualart and M. Sanz-Solé).
  4. Varadhan estimates for the density of the solution to a parabolic stochastic partial differential equation, Stochastic Processes and their Applications, Proceedings of the fifth Gregynog Symposium, World Scientific (1996), p. 330-342 (with M. Sanz-Solé).
  5. Uniform large deviations for parabolic SPDEs and applications, Stochastic Processes and their Applications 72 (1997), p. 161-186 (with F. Chenal) File.pdf.
  6. Large Deviations for Stochastic flows and anticipating SDEs in Besov-Orlicz spaces, Stochastics and Stochastic Reports 63 (1998), p. 267-302, (with M. Mellouk).
  7. Large deviations for the Boussinesq equation under random influences, Stochastic Processes and their Applications 119-6, (2009), p. 2052-2081 (avec J. Duan). You can read this paper with the following liink DOI or the author's file
  8. Stochastic 2D hydrodynamical type systems: Well posedness and large deviations, Applied Mathematics and Optimization (to appear), (with I. Chueshov). You can read this paper using the following link DOI or with the author's file
  9. Large deviation principle and inviscid shell models, Electronic Journal of Probability Vol 14 n 89, (2009), p. 2551-2589 (with H. Bessaih) File.pdf You can also read this paper using the link
  10. Inviscid Large deviation principle and the 2D Navier Stokes equations with a free boundary condition, sumitted for publication, preprint hal-00537662 and arXiv:1011.4351, November 18, 2010 (with H. Bessaih).

Support Theorems and Wong Zakai Approximation

  1. Support theorems for a class of anticipating stochastic differential equations, Stochastics and Stochastics Reports 39 (1992), p. 1-24 (with D. Nualart).
  2. Un théorème de support pour une équation aux dérivées partielles stochastiques hyperbolique, C. R. Acad. Sc. Paris, Série I, t. 315 (1992), p. 615-618 (with M. Sanz-Solé).
  3. On the support of a Skorohod anticipating stochastic differential equation, Barcelona Seminar on Stochastic Analysis, Progress in Probability Vol. 32, p. 103-131, Birkhauser Verlag, Basel (1993) (with M. Sanz-Solé).
  4. The support of the solution to a hyperbolic SPDE, Probability Theory and Related Fields 98 (1994), p. 361-387 (with M. Sanz-Solé) File.dvi
  5. A simple proof of the support theorem for diffusion processes, Séminaire de Probabilités XXVIII (1994), Lecture Notes in Mathematics 1583, p. 36-48 (with M. Sanz-Solé).
  6. Approximation and support theorem in Holder norm for parabolic stochastic partial differential equations, The Annals of Probability 23 (1995), p. 178-222 (with V. Bally and M. Sanz-Solé).
  7. Approximation and support theorem for a two-space dimensional wave equation, Bernoulli 6 (5) (2000), p. 887-915 (with M. Sanz-Solé).
  8. A support theorem for a generalized Burgers equation, Potential Analysis 15 (2001), p. 361-408 (with C. Cardon-Weber). Yo can read this paper using the following link DOI
  9. Stochastic 2D hydrodynamical systems: Wong-Zakai approximation and Support theorem, Stochastic Analysis ans Applications, Volume 29, Issue 4 (2011), p. 570-611 (with I. Chueshov). You can read this paper using the following link DOI or with the author's file

Exisence, Regularity and Discretization Schemes for Stochastic PDEs

  1. A stochastic wave equation in two space dimension: smoothness of the law, The Annals of Probability 27 (1999), p. 803-844 (with M. Sanz-Solé).
  2. On a stochastic wave equation in two space dimension: regularity of the solution and its density, Stochastic Processes and their Applications 86 (2000), p. 141-162 (with P.L. Morien).
  3. On a non linear stochastic wave equation in the plane: existence and uniqueness of the solution, The Annals of Applied Probability 11 (2001), p. 922-951 (with P.-L. Morien).
  4. On strongly Petrovskii's parabolic SPDEs in arbitrary dimension and application to the stochastic Cahn-Hilliard equation, Journal of Theoretical Probability 17-1 (2004), p. 1-49 (with C. Cardon-Weber). You can read the abstract on the following Kluwer
  5. On implicit and explicit discretization schemes for parabolic SPDEs in any dimension, Stochastic Processes and their Applications 115-7 (2005), p. 1073-1106 (with P.L. Morien) You can read this paper using the following link DOI or the author's file.
  6. On discretization schemes for stochastic evolution equations, Potential Analysis Vol. 23 (2005), p. 99-134 (with I. Gyongy). You can read this paper using the following link DOI or with the author's file
  7. Rate of Convergence of Implicit Approximations for stochastic evolution equations, Stochastic Differential Equations: Theory and Applications A volume in Honor of Professor Boris L. Rosovskii, Interdisciplinary Mathematical Sciences, Vol 2 World Scientific (2007), p. 281-310 (with I. Gyongy). You can read this paper using the author's file
  8. Rate of Convergence of Space Time Approximations for stochastic evolution equations, Potential Analysis Vol. 30-1 (2009), p. 29-64 (with I. Gyongy). You can read this paper on DOI or with the author's file.
 
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