Publications

2016

• 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.
• 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
• 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
• Generalized Arbitrage-Free SVI Volatility Surfaces
  
  • Guo Gaoyue
  • Jacquier Antoine
  • Martini Claude
  • Neufcourt Leo
  SIAM Journal on Financial Mathematics, Society for Industrial and Applied Mathematics, 2016, 7 (1), pp.619-641. In this article we propose a generalisation of the recent work of Gatheral and Jacquier on explicit arbitrage-free parameterisations of implied volatility surfaces. We also discuss extensively the notion of arbitrage freeness and Roger Lee's moment formula using the recent analysis by Roper. We further exhibit an arbitrage-free volatility surface different from Gatheral's SVI parameterisation. (10.1137/120900320)
  DOI : 10.1137/120900320
• Jan de Leeuw and the French School of Data Analysis
  
  • Husson François
  • Josse Julie
  • Saporta Gilbert
  Journal of Statistical Software, University of California, Los Angeles, 2016, 73 (6), pp.16 p.. The Dutch and the French schools of data analysis differ in their approaches to the question: How does one understand and summarize the information contained in a data set? The commonalities and discrepancies between the schools are explored here with a focus on methods dedicated to the analysis of categorical data, which are known either as homogeneity analysis (HOMALS) or multiple correspondence analysis (MCA). (10.18637/jss.v073.i06)
  DOI : 10.18637/jss.v073.i06
• New transmission condition accounting for diffusion anisotropy in thin layer applied to diffusion MRI
  
  • Caubet Fabien
  • Haddar Houssen
  • Li Jing Rebecca
  • Nguyen Dang Van
  ESAIM: Mathematical Modelling and Numerical Analysis, Société de Mathématiques Appliquées et Industrielles (SMAI) / EDP, 2016 (51), pp.1279--1301. The Bloch-Torrey Partial Differential Equation (PDE) can be used to model the diffusion Magnetic Resonance Imaging (dMRI) signal in biological tissue. In this paper, we derive an Anisotropic Diffusion Transmission Condition (ADTC) for the Bloch-Torrey PDE that accounts for anisotropic diffusion inside thin layers. Such diffusion occurs, for example, in the myelin sheath surrounding the axons of neurons. This ADTC can be interpreted as an asymptotic model of order two with respect to the layer thickness and accounts for water diffusion in the normal direction that is low compared to the tangential direction. We prove uniform stability of the asymptotic model with respect to the layer thickness and a mass conservation property. We also prove the theoretical quadratic accuracy of the ADTC. Finally, numerical tests validate these results and show that our model gives a better approximation of the dMRI signal than a simple transmission condition that assumes isotropic diffusion in the layers. (10.1051/m2an/2016060)
  DOI : 10.1051/m2an/2016060