Contrat doctoral Probabilités et statistiques Orléans Tours M/F

Role: Contrat doctoral Probabilités et statistiques Orléans Tours M/F
Organization: CNRS - National Center for Scientific Research
Department: Institut Denis Poisson
Location: Orléans, France
Contract Type: Temporary, Full-time (35 hours/week)
Start Date: 1 Oct 2026
Application Deadline: 26 Jun 2026 - 23:59 (UTC)

Role Overview:
Research work in mathematics. PhD Topic: Persistence Properties of Random Walks and Autoregressive Processes on ℝ.
Proposed by L. Delsol & M. Zani (University of Orléans) and M. Peigné & K. Raschel (University of Tours).

Responsibilities (Research Questions):
1. Extending Universality Results: Extend universality results to distributions with unbounded support that do not necessarily admit a density with respect to the Lebesgue measure. This requires extending results from previous work on the fluctuations of random walks constructed from triangular arrays, adapting the approach to the specific features of the autoregressive model.
2. Persistence Probability for Oscillating Random Walks: Investigate the behavior of the persistence probability as n → ∞ for "oscillating" random walks, where increments are governed by distinct probability measures on ℝ⁺ and ℝ⁻. The approach relies on the renewal theory of aperiodic sequences of operators. Applications include population dynamics in non-homogeneous random environments.
3. Statistical Tests for Oscillating Random Walks: Develop statistical tests for these models, including estimation of the means and variances of each increment distribution and estimation of the parameters of the limiting law. This work aligns with the theory of statistical testing for autoregressive systems exhibiting transition phenomena and builds on recent results on statistical tests for skew Brownian motion.
4. Persistence Probabilities for Higher-Dependence Autoregressive Processes: Study persistence probabilities for autoregressive processes with a higher dependence index. Explore connections with random walks in cones. This represents a new and broad research direction, adaptable depending on the progress of the doctoral student.

Supervision:
• L. Delsol: 25%
• M. Zani: 30%
• M. Peigné: 25%
• K. Raschel: 20%

Requirements and Qualifications:
• Education Level: Master Degree or equivalent in Mathematics or History (History of science).
• Research Experience: None required.
• Languages: French (Basic level).

What They Offer:
• Full-time temporary contract (35 hours per week).
• Research position within the Institut Denis Poisson (CNRS).
• Supervision by a team of four researchers from the Universities of Orléans and Tours.

Application Details:
Website: https://emploi.cnrs.fr/Offres/Doctorant/UMR7013-MARPEI-004/Default.aspx