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Stochastic and deterministic analysis for irregular models

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)

Articles published in Agência FAPESP Newsletter about the research grant:
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VEICULO: TITULO (DATA)
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Scientific publications
(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)
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., . (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., . (20/04426-6, 22/03379-0)
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., . (22/03379-0, 20/04426-6)