Filtrage Stochastique

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    In brief

  • Code : N9EN21B


This course provides theoretical and practical background on stochastic filtering and modelling


The forecast step for Markov processesis is described in the deterministic and the stochastic frameworks following a similar approach: the dynamics of the uncertainty is deduced from the semi-group acting on observable functions, that leads to the equation of Liouville (deterministic) or Fokker-Planck (stochastic)by duality. Ensemble prediction is then introduced and justified from the weak interpretation of the uncertainty dynamics. The Itô calculus is first introduced from numerical experiments (Itô fomula, integration of stochastic differential equation, weak/strong convergence of numerical schemes) and from integral path leading to the continuous limit of the discret 4DVar cost function. The Stratonovitch and Itô integrals are compared for their use in stochastic modelling ofa timely correlated/decorrelated multiplicative noise. Infinite dimensional system will be considered in the deterministic case.


G. Pavliotis and A. Stuart, Multiscale Methods: Averaging and Homogenization. Springer, 2008.

D. J. Higham, “An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations,” SIAM REVIEW, vol. 43, pp. 525–546, 2001.

Oksendal, Stochastic differential equations. Springer, 2003.

A. Jazwinski, Stochastic Processes and Filtering Theory. Dover Publications, 2007, p. 400.


Applied mathematics ; Programming in Python ; Numerical solution of PDEs




The National Institute of Electrical engineering, Electronics, Computer science,Fluid mechanics & Telecommunications and Networks

2, rue Charles Camichel - BP 7122
31071 Toulouse Cedex 7, France

+33 (0)5 34 32 20 00


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