arXiv subjects

Tristan Haugomat

Publications and source records attributed to Tristan Haugomat.

5 recordsLinked to original sources

arXiv2026

On the calibration of survival models with competing risks

Survival analysis deals with modeling the time until an event occurs, and accurate probability estimates are crucial for decision-making, particularly in the competing-risks setting where multiple events are possible. While recent work has addressed calibration in standard survival analysis, the competing-risks setting remains under-explored as it is harder (the calibration applies to both probabilities across classes and time horizon). We show that existing calibration measures are not suited to the competing-risk setting and that recent models do not give well-behaved probabilities. To address this, we introduce a dedicated framework with two novel calibration measures that are minimized for oracle estimators (i.e., both measures are proper). We also introduce some methods to estimate, test, and correct the calibration. Our recalibration methods yield good probabilities while preserving discrimination.

stat.ME↗

arXiv2017

Locally Feller processes and martingale local problems

This paper is devoted to the study of a certain type of martingale problems associated to general operators corresponding to processes which have finite lifetime. We analyse several properties and in particular the weak convergence of sequences of solutions for an appropriate Skorokhod topology setting. We point out the Feller-type features of the associated solutions to this type of martingale problem. Then localisation theorems for well-posed martingale problems or for corresponding generators are proved.

math.PR↗

arXiv2017

Lévy-type processes: convergence and discrete schemes

We characterise the convergence of a certain class of discrete time Markov processes toward locally Feller processes in terms of convergence of associated operators. The theory of locally Feller processes is applied to Lévy-type processes in order to obtain convergence results on discrete and continuous time indexed processes, simulation methods and Euler schemes. We also apply the same theory to a slightly different situation, in order to get results of convergence of diffusions or random walks toward singular diffusions. As a consequence we deduce the convergence of random walks in random medium toward diffusions in random potential.

math.PR↗

arXiv2017

Local Skorokhod topology on the space of cadlag processes

We modify the global Skorokhod topology, on the space of cadlag paths, by localising with respect to space variable, in order to include the eventual explosions. The tightness of families of probability measures on the paths space endowed with this local Skorokhod topology is studied and a characterization of Aldous type is obtained. The local and global Skorokhod topologies are compared by using a time change transformation. A number of results in the paper should play an important role when studying Lévy-type processes with unbounded coefficients by martingale problem approach.

math.PR↗

arXiv2014

On the a.c. spectrum of 1D discrete Dirac operator

In this paper, under some integrability condition, we prove that an electrical perturbation of the discrete Dirac operator has purely absolutely continuous spectrum for the one dimensional case. We reduce the problem to a non-self-adjoint Laplacian-like operator by using a spin up/down decomposition and rely on a transfermatrices technique.

math-ph↗