Stochastic and deterministic analysis for irregular models

• Grant number: 22/03379-0
• Support Opportunities: Regular Research Grants
• Start date: April 01, 2023
• End date: March 31, 2027
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Agreement: ANR
• Principal Investigator: Christian Horacio Olivera
• Grantee: Christian Horacio Olivera
• Principal researcher abroad: Francesco Russo
• Institution abroad: Ecole Nationale Supérieure des Techniques Avancées (ENSTA), France
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated researchers: Diego Sebastian Ledesma ; Gabriela Del Valle Planas ; Lucas Catão de Freitas Ferreira ; Paulo Regis Caron Ruffino ; Pedro Jose Catuogno

Abstract

The ambition of the project consists in describing and investigate irregular phenomena arising from hydrodynamics, oncology, economics, or complex systems, from a macroscopic-microscopic point of view. We will take advantage of the complementarity of deterministic and stochastic analysis. Many difficulties appear such as discontinuous (even distributional) coefficients, jumps, rough behaviour of stochastic processes, non-conservativity, and lack of Markovian character. Typical examples corresponding to real applications areKeller-Segel models, Burgers-Huxley, fast and superfast diffusions, porous media type equations, self-organized criticality, McKean SDEs in random environment, Vlasov-Navier-Stokes, Hamilton-Jacobi PDEs. We are guided by three main motivations.1) Deterministic macroscopic modeling and mathematical theory.2) Stochastic microscopic modeling involving extended McKean probabilistic representations of irregular models together with particle approximations.3) Numerical simulation: to provide approximation schemes for non-linear PDEs potentially involving path-dependent coefficients, and random environment. (AU)

Scientific publications

(5)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

SIMON, MARIELLE; OLIVERA, CHRISTIAN. Microscopic derivation of non-local models with anomalous diffusions from stochastic particle systems. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, v. 253, p. 19-pg., 2024-12-28. (22/03379-0, 20/04426-6)

KNORST, JOSUE; OLIVERA, CHRISTIAN; DE SOUZA, ALEXANDRE B.. Convergence rate for moderate interaction particles and application to mean field games. Journal of Mathematical Analysis and Applications, v. 549, n. 2, p. 20-pg., 2025-05-02. (22/13413-0, 20/04426-6, 22/03379-0)

CORREA, JESUS; OLIVERA, CHRISTIAN. From Particle Systems to the Stochastic Compressible Navier-Stokes Equations of a Barotropic Fluid. JOURNAL OF NONLINEAR SCIENCE, v. 35, n. 3, p. 47-pg., 2025-06-01. (20/04426-6, 22/03379-0)

CORREA, JESUS M.; ACEVEDO, JUAN DAVID LONDONO; OLIVERA, CHRISTIAN. From Hamiltonian systems to compressible Euler equation driven by additive Holder noise. INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, v. N/A, p. 18-pg., 2025-04-05. (20/04426-6, 22/03379-0)

OLIVERA, CHRISTIAN; TUDOR, CIPRIAN A.. Temporal quadratic and higher order variation for the nonlinear stochastic heat equation and applications to parameter estimation. Annali di Matematica Pura ed Applicata, v. N/A, p. 29-pg., 2025-05-31. (20/04426-6, 22/03379-0)