Feynman-Kac measures and Interacting Particle systems :

Selected studies on : Measure valued processes and stochastic partial differential equations

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• Software BiiPS

  
  The software BIIPS is a general software developed by the INRIA team ALEA for bayesian inference with interacting particle systems, a.k.a. Sequential Monte Carlo methods. A demonstration of the BiiPS software for estimating the stochastic volatility of financial data can be found in
  
  
  • BIIPS : Bayesian inference with interacting Particle Systems in Finance,
    
  
  
  
  INRIA project manager : F. Caron, Design and developement engineer : A. Todeschini, Project contributors : P. Del Moral & P. Legrand, Logo designer : Timothée Del Moral.
  
  
  
  
  
  
  
  
  

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• Branching and Interacting particle approximations

  
  
  • 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)
    
    
  • Particle Methods: An introduction with applications (Pierre Del Moral, Arnaud Doucet) HAL-INRIA RR-6991 [50p] (2009), 2008 Machine Learning Summer School, Springer LNCS/LNAI Tutorial book no. 6368 (2010-2011).
    
    
  • Nonlinear Filtering : Interacting Particle Resolution. (Del Moral P. Markov Processes and Related Fields, vol. 2, no; 4, pp. 555-580 (1996)).
    
    
  • 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 the Robustness of the Snell Envelope (P. Del Moral, P. Hu, N. Oudjane, and B. Rémillard SIAM Journal of Financial Maths (2011)).
    
    
  • 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)).
    
    
  • Solutions for diffuse optical tomography using the Feynman-Kac formula and interacting particle method (Nannan Cao, Mathias Ortner, and Arye Nehorai, Department of Electrical and Systems Engineering, Washington University)
    
    
  • Un Theoreme Limite de Systeme de Particules Aleatoires et Processus de Branchement a Valeurs Mesures (Isamu Doku, Saitama Univ., Fac. Educ. 2007)
    
    
  • Rates for branching particle approximations of continuous-discrete filters (Michael A. Kouritzin and Wei Sun, Alberta Univ. Tech. report 2004 )
    
    
  • Limit theorems for some branching measure-valued processes (Bertrand Cloez, 2011 )
    
    
  • Linear Variance Bounds for Particle Approximations of Time-Homogeneous Feynman-Kac Formulae (Nick Whiteley, N. Kantas, A. Jasra, 2011)
    
    
  • Using systematic sampling selection for Monte Carlo solutions of Feynman-Kac equations (I. Gentil, B. Remillard, Adv. Appl. Proba. 2008)
    
    
  • A Mean Field Theory of Nonlinear Filtering (Pierre Del Moral, Frédéric Patras, Sylvain Rubenthaler HAL-INRIA RR-6437 [39p], (Feb. 2008); Oxford Handbook of Nonlinear Filtering, pages 1-39. Oxford University Press, (2011)).
    
    
  • A non asymptotic variance theorem for unnormalized Feynman-Kac particle models (Frédéric Cerou, Pierre Del Moral, Arnaud Guyader HAL-INRIA RR-6716 [29p], [submitted] (Nov. 2008); Annales de l'Institut Henri Poincaré Probab. Statist. Volume 47, Number 3, 629-649 (2011).).
    
  
  

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• Interacting Markov Chain Monte Carlo Methods

  
  
  • Interacting Markov Chain Monte Carlo Methods For Solving Nonlinear Measure-Valued Equations (P. Del Moral, A. Doucet) HAL-INRIA RR-6435 [48p], (Feb. 2008). The Annals of Applied Probability, Vol. 20, No. 2, 593-639 (2010).
    
    
  • A Functional Central Limit Theorem for a Class of Interacting Markov Chain Monte Carlo Models (B. Bercu, P. Del Moral, A. Doucet) HAL-INRIA RR-6436 [33p], (Feb. 2008); Electronic Journal of Probability, Vol. 14, Paper no. 73, pages 2130-2155 (2009).
    
    
  • Fluctuations of Interacting Markov Chain Monte Carlo Models (B. Bercu, P. Del Moral, A. Doucet) HAL-INRIA RR-6438 [28p], [submitted] (Feb. 2008).
    
    
    
    
    
    
    
  
  

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• Stochastic models and stability analysis

  
  
  • Fractional Generalization of Kac Integral(Vasily E. Tarasov, and George M. Zaslavsky; Courant Institute, Skobeltsyn Institute of Nuclear Physics, Moscow State University, and Department of Physics, New York University 2007)
    
    
  • The stability of conditional Markov processes and Markov chains in random environments (Ramon van Handel, Princeton University; Annals of Probability 2009)
    
    
  • On the stability of interacting processes with applications to filtering and genetic algorithms (Del Moral P., Guionnet A.) Annales de l'Institut Henri Poincaré, Vol. 37, No. 2, 155-194 (2001).
    
    
  • A Continuous-State Version of Discrete Randomized Shortest-Paths, with Application to Path Planning (Silvia Garcia-Diez, Eric Vandenbussche and Marco Saerens 2011)
    
    
  • QIB: Connecting Feynman Path Integrals to Biophysical Problems (Alexander Pease, Princeton Univ. 2011)
    
    
  • Brownian Motion (Peter Morters and Yuval Peres, with an appendix by Oded Schramm and Wendelin Werner)
    
    
  • Numerical methods for sensitivity analysis of Feynman-Kac models (Pierre-Arnaud Coquelin, Romain Deguest, Remi Munos, Hal-INRIA-2007)
    
    
  • Towards pathwise stochastic fast dynamo in magneto-hydrodynamics (S.B. Hasra, F. Viens)
    
    
  • A continuous stochastic maturation model (Djalil Chafai and Didier Concordet 2006)
    
    
  • Numerical Solution of a Class of SPDEs with Applications to Filtering (T. Kurtz, J. Xiong; Wisconsin Univ.)
    
    
  • A Stochastic Evolution Equation Arising from The Fluctuation of a Class of Interacting Particle Systems (T. Kurtz, J. Xiong; Wisconsin Univ.)
    
    
  • Asymptotic Stability of Non Linear Semigroup of Feynman-Kac Type. (Del Moral P., Miclo L.) Publications du LSP-CNRS No 04-99 (1999), Annales de la Faculté 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., Guionnet A.) Annales de l'Institut Henri Poincaré, Vol. 37, No. 2, 155-194 (2001)
    
    
  • 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).
    
    
    
    
    

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