Feynman-Kac-Schrodinger Semigroups,
Genealogical and Interacting Particle interpretations.

Nonlinear Analysis and Asymptotic Theory (some selected studies)

Lecture notes

• Horizon Maths, Les maths se devoilent aux industriels; Fondation Science Maths de Paris, Tour AREVA, dec. 2011. (programme) ( lecture notes (in french) & the presentation video (in french) )
  
• Sino-French Summer Institute 2011.Beijing, China, June 13-25, 2011 :
  
  
  • lecture 1 (Introduction)
  • lecture note 2 (Application domains)
  • and lecture 3 (Theoretical analysis)
  
  
• INRIA Workshop on Statistical Learning Institut Henri Poincaré Paris, December 5-6, 2011 ( lecture notes )
  
• Isaac Newton Institute for Mathematical Sciences, Workshop on filtering. June 2010 (lecture notes) & (presentation video)
• University of Cambridge, Statistics Laboratory seminar, Feb. 2010. (lecture notes)
  
• 10th Machine Learning summer school, September 1-15th, 2008. (lecture notes)
  
• Opening workshop, Sequential Monte Carlo Methods, SAMSI, Duke Univ. September 7-10th, 2008. (lecture notes)
  
• CMAP Seminar in Polytechnique, 2011.
• Analysis and Probability in Nice :
  
  
  • lecture 2008 (stability of Feynman-Kac semigroups)
  • lecture 2010 (Concentration inequalities)
  
  
  

Tutorials & Research Books

• Feynman-Kac Formulae, Genealogical and Interacting Particle Systems with Applications Del Moral P., Springer New York; Springer Heidelberg, Series: Probability and its Applications, [585 pages] (April 2004).
  
  
• Research habilitation (HDR, May 2002)
  
  
• Simulation and Stochastic Algorithms. An introduction with applications
  Bartoli N., Del Moral P., Cépaduès Editions.
  
  
• Branching and Interacting Particle Systems Approximations of Feynman-Kac Formulae with Applications to Non-Linear Filtering Del Moral P., Miclo L., Séminaire de Probabilités XXXIV, Ed. J. Azéma and M. Emery and M. Ledoux and M. Yor,
  Lecture Notes in Mathematics, Springer-Verlag Berlin, Vol. 1729, 1-145 (2000).
  
  
  
• Particle Methods: An introduction with applications
  HAL-INRIA RR-6991 [50p] (2009) (P. Del Moral, A. Doucet) 2008 Machine Learning Summer School, Springer LNCS/LNAI Tutorial book no. 6368 (2010-2011).
  
  
• Pierre Del Moral, Peng Hu, Liming Wu
  On the concentration properties of Interacting particle processes HAL-INRIA RR-7677 (2011),
  Foundations and Trends in Machine Learning, Vol. 3, No. 3 - 4, 225-389 (2012). (online article, 167 pages)
  
  

Propagation-of-chaos estimates

• Coalescent tree based functional representations for some Feynman-Kac particle models (preliminary version)
  P. Del Moral, F. Patras, and S. Rubenthaler) Annals of Applied Probability, Vol. 19, No. 2, pages 1--50 (2009)
  
  
  
• A non asymptotic variance theorem for unnormalized Feynman-Kac particle models
  Frederic Cerou, Pierre Del Moral, Arnaud Guyader
  HAL-INRIA RR-6716 [29p], [submitted] (Nov. 2008).
  
  
• Coalescent tree based functional representations for some Feynman-Kac particle models
  Del Moral P., Patras F., Rubenthaler S.
  HAL INRIA and Publication du Lab. J. A. Dieudonné, Univ. Nice-Sophia Antipolis [55p] (2006).
  To appear in the Annals of Applied Probability (2009).
  
  
• Sharp Propagations of Chaos Estimates for Feynman-Kac particle Models
  Del Moral, P., Doucet A., Peters G.W.
  Probability Theory and its Applications, SIAM, vol. 51, no. 3 (2006).
  
  
• Precise Propagations of Chaos Estimates for Feynman-Kac and Genealogical Particle Models
  Del Moral P., Miclo L., Viens F.
  Technical Report, Purdue University, [29p], [submitted] (2003).
  
  
• Genealogies and Increasing Propagations of Chaos for Feynman-Kac and Genetic Models.
  Del Moral P., Miclo L.
  Annals of Applied Probability , vol. 11, No. 4, pp. 1166-1198 (2001).
  
  
• On the strong propagation of chaos for interacting particle approximations of Feynman-Kac formulae.
  Del Moral P., Miclo L.
  Publications du Laboratoire de Statistiques et Probabilités, Toulouse III, No 08-00 (2000).
  
  
  

Central Limit Theorems

• Some fluctuation theorems (including path space and ABC style models)

  • A Central Limit Theorem for Non Linear Filtering using Interacting Particle Systems.
    Del Moral, P., Guionnet A.
    Annals of Applied Probability, Vol. 9, No. 2, 275-297 (1999).
    
    
  • On the Convergence and the Applications of Empirical Processes for Interacting Particle Systems and Nonlinear Filtering.
    Del Moral, P., Ledoux M.
    Journal of Theoret. Probability, Vol. 13, No. 1, 225-257 (2000).
    
    
  • Interacting Particle Filtering With Discrete Observations.
    Del Moral, P., Jacod J.
    Sequential Monte Carlo Methods in Practice, pp. 43-77, Statistics for Engineering and Information Science. Springer. Eds. A. Doucet, J. F. G. de Freitas, N. J. Gordon. (2001).
    
    
  • The Monte-Carlo Method for filtering with discrete time observations. Central Limit Theorems.
    Del Moral, P., Jacod J.
    The Fields Institute Communications, Numerical Methods and Stochastics,
    Ed. T.J. Lyons, T.S. Salisbury, American Mathematical Society, (2002).
    
    
  • Genealogical Particle Analysis of Rare Events
    Del Moral P., Garnier J.,
    The Annals of Applied Probability Vol. 15, pp. 2496-2534 (2005).
    

• Central Limit Theorems for adaptive sampling schemes

  • On Adaptive Resampling Procedures for Sequential Monte Carlo Methods
    Pierre Del Moral, Arnaud Doucet, Ajay Jasra
    HAL-INRIA RR-6700 [46p], (Oct. 2008).
  
  

• Unbounded functions : L2-functions and algebrae of functions with growth conditions

  • A Central Limit Theorem for Non Linear Filtering using Interacting Particle Systems.
    Del Moral, P., Guionnet A.
    Annals of Applied Probability, Vol. 9, No. 2, 275-297 (1999).
    
    
  • On the Convergence and the Applications of Empirical Processes for Interacting Particle Systems and Nonlinear Filtering.
    Del Moral, P., Ledoux M.
    Journal of Theoret. Probability, Vol. 13, No. 1, 225-257 (2000).
    
    
  • The Monte-Carlo Method for filtering with discrete time observations. Central Limit Theorems.
    Del Moral, P., Jacod J.
    The Fields Institute Communications, Numerical Methods and Stochastics,
    Ed. T.J. Lyons, T.S. Salisbury, American Mathematical Society, (2002).

• Berry Esseen Theorem

  • A Berry-Esseen theorem for Feynman-Kac and interacting particle models.
    Del Moral, P., Tindel S.
    Annals of Applied Probability vol. 15, No. 1B, 941-962 (2005).

• Moderate deviations

  • Moderate Deviations for Mean Field Particle Models P. Del Moral, S. Hu, L.M. Wu
    HAL-INRIA 00687827 [37p], (April 2012) [submitted].
    
    

• Continuous time models

  • Particle approximations of Lyapunov exponents connected to Schrodinger operators and Feynman-Kac semigroups.
    (Del Moral, P., Miclo L.) ESAIM: Probabilités et Statistiques(2003)

• Donsker theorems

  • On the Convergence and the Applications of Empirical Processes for Interacting Particle Systems and Nonlinear Filtering.
    (Del Moral, P., Ledoux M.) Journal of Theoret. Probability, Vol. 13, No. 1, 225-257 (2000).

• U-Statistics

  • Convergence of U-statistics for interacting particle systems (HAL-INRIA RR-6966 (2009))
    (P. Del Moral, F. Patras, S. Rubenthaler), Journal of Theoretical Probability, DOI: 10.1007/s10959-011-0355-6, (2011).

• Path space models

  A Central Limit Theorem for Non Linear Filtering using Interacting Particle Systems.
  (Del Moral, P., Guionnet A.) Annals of Applied Probability, Vol. 9, No. 2, 275-297 (1999).

• Non asymptotic variance estimates

  • A non asymptotic variance theorem for unnormalized Feynman-Kac particle models
    (HAL-INRIA RR-6716 (2008)). (F. Cerou, P. Del Moral, A. Guyader) Ann. Inst. H. Poincaré Probab. Statist. Volume 47, Number 3, 629-649 (2011).

• Interacting MCMC models

  • A Functional Central Limit Theorem for a Class of Interacting Markov Chain Monte Carlo Models (HAL-INRIA RR-6436 (2008))
    (B. Bercu, P. Del Moral, A. Doucet) Electronic Journal of Probability. Vol. 14, Paper no. 73, pages 2130-2155 (2009).

Large Deviation Principles

• Large deviations for interacting processes in the strong topology.
  Dawson D. and Del Moral P.
  Statistical Modeling and Analysis for Complex Data Problem.
  P. Duchesne and B. Rémillard Editors, pp. 179-209, Springer (2005).
  
  
• A note on Laplace-Varadhan's integral lemma.
  Del Moral P. and Zajic T.
  Bernoulli, vol.9, no. 1, pp. 49--65 (2003).
  
  
• Large Deviations for Interacting Particle Systems. Applications to Non Linear Filtering Problems.(corrected version )
  Del Moral P., Guionnet A.
  Stochastic Processes and their Applications 78, pp. 69-95 (1998).
  
  
• On Adaptive Resampling Procedures for Sequential Monte Carlo Methods
  Pierre Del Moral, Arnaud Doucet, Ajay Jasra
  HAL-INRIA RR-6700 [46p], (Oct. 2008).
  
  

Convergence of empirical processes

Moderate deviations

• Moderate Deviations for Mean Field Particle Models P. Del Moral, S. Hu, L.M. Wu
  HAL-INRIA 00687827 [37p], (April 2012) [submitted].
  
  

• On the Convergence and the Applications of Empirical Processes for Interacting Particle Systems and Nonlinear Filtering.
  (Del Moral, P., Ledoux M.) Journal of Theoret. Probability, Vol. 13, No. 1, 225-257 (2000).
  
  
• Concentration Inequalities for Mean Field Particle Models (HAL-INRIA RR-6901)
  (P. Del Moral, E. Rio) Ann. Appl. Probab. Volume 21, Number 3, 1017-1052. (2011).
  
  
• Branching and Interacting Particle Systems Approximations of Feynman-Kac Formulae with Applications to Non-Linear Filtering Del Moral P., Miclo L., Séminaire de Probabilités XXXIV, Ed. J. Azéma and M. Emery and M. Ledoux and M. Yor,
  Lecture Notes in Mathematics, Springer-Verlag Berlin, Vol. 1729, 1-145 (2000).
  
  
  
• On the concentration properties of Interacting particle processes P. Del Moral, P. Hu, L.M. Wu. HAL-INRIA RR-7677 (2011) [122p],
  To appear in Foundations and Trends in Machine Learning (2011-2012).
  
  

Concentration analysis

• Annealed Feynman-Kac Models.
  (Del Moral P. and Miclo L.) Communications in Mathematical Physics, vol. 235, no. 2, pp.191--214 (2003).
  
  
• On the Convergence and the Applications of the Generalized Simulated Annealing.
  Del Moral P., Miclo L.,
  SIAM Journal on Control and Optimization, Vol. 37, No. 4, 1222-1250, (1999).
  
  
• Concentration Inequalities for Mean Field Particle Models (HAL-INRIA RR-6901)
  (P. Del Moral, E. Rio) Ann. Appl. Probab. Volume 21, Number 3, 1017-1052. (2011).
  
  
• On the concentration properties of Interacting particle processes P. Del Moral, P. Hu, L.M. Wu. HAL-INRIA RR-7677 (2011) [122p],
  To appear in Foundations and Trends in Machine Learning (2011-2012).
  
  

Stability and Contraction analysis

• The convergence to equilibrium of neutral genetic models
  Del Moral P., Miclo L., Patras F., Rubenthaler S.
  HAL Archive et Publication du Lab. J.A. Dieudonne Univ. Nice-Sophia Antipolis [28pp] (2007).
  
  
• Particle approximations of a class of branching distribution flows arising in multi-target tracking
  (F. Caron, P. Del Moral, A. Doucet, and M. Pace) (HAL-INRIA RR-7233 (2010)) [29p], SIAM J. Control Optim. 49, pp. 1766-1792 (2011).
  
  
• On the Stability and the Approximation of Branching Distribution Flows, with Applications to Nonlinear Multiple Target Filtering
  (F. Caron, P. Del Moral, M. Pace, and B.-N. Vo) (HAL-INRIA RR-7376) [50p]. (short version) Stoch. Analysis and Applications (2011).
  
  
• Stability of Feynman-Kac formulae with path-dependent potentials,
  (P. Del Moral, N. Chopin, S. Rubenthaler) Stochastic Processes and their Applications, 121, 38-60 (2011).
  
  
• Contraction properties of Markov kernels.
  (Del Moral P., Ledoux M. and Miclo L.) Probab. Theory and Related Fields, vol. 126, pp. 395-420, (2003).
  
  
• Asymptotic Stability of Non Linear Semigroup of Feynman-Kac Type.
  Del Moral P. and Miclo L.
  Annales de la Facult\'e des Sciences de Toulouse, vol.11,no.2, pp. (2002).
  
  
• On the stability of interacting processes with applications to filtering and genetic algorithms
  Del Moral P. and Guionnet A.
  Annales de l'Institut Henri Poincaré, Vol. 37, No. 2, 155-194 (2001).
  
  
  
  

Measure Valued Processes, Stochastic PDE's

• Nonlinear Filtering : Interacting Particle Resolution.
  Del Moral P.
  Markov Processes and Related Fields, vol. 2, no; 4, pp. 555-580 (1996).
  
  
• On the Conditional Distributions of Spatial Point Processes
  (HAL-INRIA RR-7232) (F. Caron, P. Del Moral, A. Doucet, and M. Pace) Adv. in Appl. Probab. Volume 43, Number 2, 301-307. (2011).
  
  
• Measure Valued Processes and Interacting Particle Systems. Application to Nonlinear Filtering Problems
  Del Moral P.
  Annals of Applied Probab, vol. 8, no. 2, pp. 1254-1278 (1998).
  
  
• On a Class of Discrete Generation Interacting Particle Systems
  Del Moral P., M. Kouritzin, L. Miclo
  Electronic Journal of Probab, vol. 6, paper 16, pp. 1-26 (2001).
  
  
• Discrete Filtering using Branching and Interacting Particle Systems
  D. Crisan, P. Del Moral, T. Lyons
  Markov Processes and Related Fields, vol. 5, no. 3, pp. 293-318 (1999).
  
  
• Branching and Interacting Particle Systems Approximations of Feynman-Kac Formulae with Applications to Non-Linear Filtering
  Del Moral P., Miclo L.,
  Séminaire de Probabilités XXXIV, Ed. J. Azéma and M. Emery and M. Ledoux and M. Yor,
  Lecture Notes in Mathematics, Springer-Verlag Berlin, Vol. 1729, 1-145 (2000).
  
  
• Interacting Particle Systems. Approaximations of the Kushner-Stratonovitch Equation
  D. Crisan, P. Del Moral, T. Lyons
  Advances in Applied Probab, vol. 31, no. 3, pp. 819-838 (1999).
  
  
• Interacting Markov Chain Monte Carlo Methods For Solving Nonlinear Measure-Valued Equations
  (HAL-INRIA RR-6435 (2008)) (P. Del Moral, A. Doucet) The Annals of Applied Probability, Vol. 20, No. 2, 593-639 (2010)
  
  
  

Some applications (see also the website on Feynman-Kac models )

• Genealogical Models in Entrance Times Rare Event Analysis
  F. Cerou, Del Moral P. Le Gland F., Lezaud P.
  Alea, Latin American Journal of Probability And Mathematical Statistics (2006).
  
  
• Sequential Monte Carlo for Rare event estimation (HAL-INRIA RR-6792 (2009))
  (F. Cerou, P. Del Moral, T. Furon, A. Guyader) Statistics and Computing, DOI: 10.1007/s11222-011-9231-6 (2011).
  
  
• Sequential Monte Carlo Methods for Option Pricing, [37p.]
  (A.Jasra, and P. Del Moral) Stoch. Analysis and Applications, Volume 29, Issue 2, 2011, Pages 292 - 316 (2011)
  
  
• Fundamentals of stochastic filtering by Alan Bain and Dan Crisan
  (P. Del Moral) Book Review [13p.], Bulletin of the American Mathematical Society (Oct. 2010).
  
  
• A Backward Particle Interpretation of Feynman-Kac Formulae(HAL-INRIA RR-7019 (07-2009))
  (P. Del Moral, A. Doucet and S. S. Singh) vol 44, no. 5, pp. 947--976 M2AN (sept. 2010)
  
  
• An Introduction to probabilistic methods, with applications
  (P. Del Moral and N. Hadjiconstantinou), vol 44, no. 5, pp. 805--830 M2AN (sept. 2010)
  
  
• Sequentially Interacting Markov chain Monte Carlo (A. Brockwell, P. Del Moral, A. Doucet)
  Technical Report UBC Vancouver (2008) Ann. Statist. Volume 38, Number 6, pp. 3387-3411. (2010)
  
  
• Sequential Monte Carlo Samplers
  Del Moral P., Doucet A., Jasra A.
  Journal of the Royal Society of Statistics, Series B. vol. 68, No. 3, pp. 411-436 (2006).
  
  
• Genealogical Particle Analysis of Rare Events
  Del Moral P., Garnier J., The Annals of Applied Probability Vol. 15, pp. 2496-2534 (2005).
  
  
• Simulation of Rare Events in Fiber Optics by Interacting Particle Systems
  Garnier J., Del Moral P.
  Optics Communications Vol. 257, pp. 205-214 (2006).
  
  
• Branching and Interacting Particle Interpretations of Rare Event Probabilities.
  Del Moral P., Lézaud P.,
  Stochastic Hybrid Systems: Theory and Applications., 51 p. (2006).
  
  
• Particle approximations of Lyapunov exponents connected to Schrodinger operators and Feynman-Kac semigroups.
  Del Moral P., Miclo L.,
  ESAIM: Probabilités et Statistiques. (2003).
  
  
• On a class of genealogical and interacting Metropolis Models.
  Del Moral P., Doucet A.
  Séminaire de Probabilités XXXVII, Ed. J. Azéma and M. Emery and M. Ledoux and M. Yor,
  Lecture Notes in Mathematics 1832, Springer-Verlag Berlin, pp. 415--446 (2003).
  
  
• On Adaptive Resampling Procedures for Sequential Monte Carlo Methods
  (P. Del Moral, A. Doucet, A. Jasra) (HAL-INRIA RR-6700) [46p], (Oct. 2008). Bernoulli (2011).<>
  
  
• An Adaptive Sequential Monte Carlo Method for Approximate Bayesian Computation
  (P. Del Moral, A. Doucet, A. Jasra) (preliminary version) Statistics and Computing (2011).
  
  
• On the Robustness of the Snell envelope
  (HAL-INRIA RR-7303 (2010)) P. Del Moral, P. Hu, N. Oudjane, B. Rémillard), SIAM Journal on Financial Mathematics, vol.2, 587-626 (2011).
  
  
• Méthodes Monte Carlo Séquentielles Pour l'Analyse Spectrale Bayesienne.
  M. Davy and P. Del Moral and A. Doucet
  XIX Colloque GRETSI, 8-11 September 2003, Paris.
  
  
• Particle Motions in Absorbing Medium with Hard and Soft Obstacles.
  Del Moral P., Doucet A.
  Stochastic Analysis and Applications, vol. 22, no. 5, (2004).
  
  
• Optimal nonlinear filtering in GPS/INS integration Carvalho H., Del Moral P., Monin A., Salut G.
  IEEE Transactions on Aerospace and Electronic Systems
  
  
• Particle resolution and non-linear signal : processing with RADAR/SONAR applications Del Moral P., J.C. Noyer, G. Rigal, Salut G. (LAAS-CNRS Toulouse)