Marushkevych, Dmytro Popier, Alexandre
Published in
Probability, Uncertainty and Quantitative Risk
We use the functional Itô calculus to prove that the solution of a BSDE with singular terminal condition verifies at the terminal time: liminft→TY(t)=ξ=Y(T)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\odds...
Fatras, Kilian Zine, Younes Flamary, Rémi Gribonval, Rémi Courty, Nicolas
Optimal transport distances are powerful tools to compare probability distributions and have found many applications in machine learning. Yet their algorithmic complexity prevents their direct use on large scale datasets. To overcome this challenge , practitioners compute these distances on minibatches i.e. they average the outcome of several small...
Blanchet-Scalliet, Christophette Dorobantu, Diana Gay, Laura
We propose an expression for the joint density / distribution function for the endpoint of an Ornstein-Uhlenbeck process and its supremum. This law is expressed as an expansion involving parabolic cylinder functions. We obtain this law faster than with a Monte Carol's method. Numerical applications illustrate the interest of this result.
Betancourt, José Bachoc, François Klein, Thierry Idier, Déborah Pedreros, Rodrigo Rohmer, Jérémy
In this article we investigate the construction of metamodels when the numerical code has functional inputs. We compare diverse Gaussian process metamodeling approaches that take into account the functional structure of the data. We discuss two methods to tune the dimension of the projection when functional inputs are decomposed on a functional bas...
Briand, Philippe Ghannoum, Abir Labart, Céline
This paper is devoted to the study of reflected Stochastic Differential Equationswith jumps when the constraint is not on the paths of the solution but acts on the law of thesolution. This type of reflected equations have been introduced recently by Briand, Elie and Hu[BEH18] in the context of BSDEs, when no jumps occur. In [BCdRGL16], the authors ...
Lupu, Titus Sabot, Christophe Tarrès, Pierre
We introduce a continuous space limit of the Vertex Reinforced Jump Process (VRJP) in dimension one, which we call Linearly Reinforced Motion (LRM) on R. It is constructed out of a convergent Bass-Burdzy flow. The proof goes through the representation of the VRJP as a mixture of Markov jump processes. As a by-product this gives a representation in ...
Goutte, Stéphane Guesmi, Khaled
International audience
Boumezoued, Alexandre Elfassihi, Amal
Since the conjecture of Richards (2008), the work by Cairns et al. (2016) and subsequent developments by Boumezoued (2016), Boumezoued et al. (2018) and Boumezoued et al. (2019), it has been acknowledged that observations from censuses have led to major problems of reliability in estimates of general population mortality rates as implemented in pra...
Loisel, Stéphane
International audience
Nikolaev, Sergei Cotin, Stéphane
Purpose:Augmented reality can improve the outcome of hepatic surgeries, assuming an accurate liver model is available to estimate the position of internal structures. While researchers have proposed patient-specific liver simulations, very few have addressed the question of boundary conditions. Resulting mainly from ligaments attached to the liver,...
