Publications

2016

• Inverse Scattering Theory and Transmission Eigenvalues
  
  • Cakoni Fioralba
  • Colton David
  • Haddar Houssem
  , 2016, 88.
• An introduction to continuous optimization for imaging
  
  • Chambolle Antonin
  • Pock Thomas
  Acta Numerica, Cambridge University Press (CUP), 2016, 25, pp.161-319. A large number of imaging problems reduce to the optimization of a cost function , with typical structural properties. The aim of this paper is to describe the state of the art in continuous optimization methods for such problems, and present the most successful approaches and their interconnections. We place particular emphasis on optimal first-order schemes that can deal with typical non-smooth and large-scale objective functions used in imaging problems. We illustrate and compare the different algorithms using classical non-smooth problems in imaging, such as denoising and deblurring. Moreover, we present applications of the algorithms to more advanced problems, such as magnetic resonance imaging, multilabel image segmentation, optical flow estimation, stereo matching, and classification. (10.1017/S096249291600009X)
  DOI : 10.1017/S096249291600009X
• The different asymptotic regimes of nearly unstable autoregressive processes
  
  • Rosenbaum Mathieu
  • Jaisson Thibault
  The Fascination of Probability, Statistics and their Applications, 2016, pp.283-301.
• Quadratic BSDEs with jumps: Related nonlinear expectations
  
  • Kazi-Tani Mohamed Nabil
  • Possamaï Dylan
  • Zhou Chao
  Stochastics and Dynamics, World Scientific Publishing, 2016, 16 (4), pp.1650012. In this article, we follow the study of quadratic backward SDEs with jumps,that is to say for which the generator has quadratic growth in the variables (z, u), started in our accompanying paper [15]. Relying on the existence and uniqueness result of [15], we define the corresponding g-expectations and study some of their properties. We obtain in particular a non-linear Doob-Meyer decomposition for g-submartingales and a downcrossing inequality which implies their regularity in time. As a consequence of these results, we also obtain a converse comparison theorem for our class of BSDEs. Finally, we provide a dual representation for the corresponding dynamic risk measures, and study the properties of their inf-convolution, giving several explicit examples. (10.1142/S021949371650012X)
  DOI : 10.1142/S021949371650012X