Control theory and stochastic analysis

Organisers: S. Kuksin, V. Nersesyan, A. Shirikyan



  1. •7 March 2016, room 05 at IHP, 3 pm

Vahagn Nersesyan (University of Versailles)

Some remarks on the ergodicity of the 2D Navier-Stokes equations. Part 2


  1. •22 February 2016, room E5.54 at University of Cergy-Pontoise,

        11am-12am & 15pm-16pm

Alexandre Boritchev (University of Lyon 1)

Convergence exponentielle et hyperbolicité des minimiseurs pour systèmes Lagrangiens aléatoires


       

Abstract: Nous regardons l'équation de Burgers stochastique aussi bien du point de vue de la dynamique Lagrangienne (comportement en temps long des courbes minimisant l'énergie) que du comportement statistique des solutions (convergence en temps long vers la mesure stationnaire). Dans les deux cas nous observons un phénomène de convergence exponentielle. Il s'agit (en partie) d'un travail en collaboration avec K. Khanin (Université de Toronto).



  1. •8 February 2016, room 05 at IHP, 3 pm

Vahagn Nersesyan (University of Versailles)

Some remarks on the ergodicity of the 2D Navier-Stokes equations. Part 1


  1. •7 December 2015, room 05 at IHP, 3 pm

Vlad Bally (University of Marne-la-Vallée)

Regularity of probability laws using integration by parts. Part 2



  1. •23 November 2015, room 421 at IHP, 3 pm

Vlad Bally (University of Marne-la-Vallée)

Regularity of probability laws using integration by parts. Part 1



  1. •9 November 2015, amphi Darboux at IHP, 3 pm

Armen Shirikyan (University of Cergy-Pontoise)

Exponential mixing for controllable differential equations. Part 2



  1. •12 October 2015, room 05 at IHP, 3 pm

Armen Shirikyan (University of Cergy-Pontoise)

Exponential mixing for controllable differential equations. Part 1


       

Abstract: This talk is devoted to describing some sufficient conditions for mixing of a stochastic flow, defined by a differential equation with random coefficients, in terms of controllability properties of an associated deterministic system. Assuming that the noise is highly degenerate, we consider two different situations in which mixing holds in the total variation and Kantorovich-Wasserstein metrics. Some applications of general results will also be discussed.


As a preliminary reading which would simplify understanding of this talk, I would recommend Sections 1.2.3, 1.2.4 and 1.3.1 of the book: S. Kuksin & A. Shirikyan, Mathematics of Two-Dimensional Turbulence, CUP, 2012.



  1. •28 September 2015, room 05 at IHP, 3 pm

Sergei Kuksin (University of Paris-7)

Existence of densities for the laws of finite-dimensional projections for solutions of a nonlinear PDE, perturbed by a lower-dimensional random force


       

Abstract: I will present the main results and ideas of my joint paper with Agrachev, Sarychev and Shirikyan "On finite-dimensional projections of distributions for solutions of randomly forced PDEs”, AIHP PR 43  (2007), 399-415, and will discuss how this work is related with the announced goals of the working-group.