Stochastic dynamics: analytical and geometrical aspects with applications

• Grant number: 20/04426-6
• Support Opportunities: Research Projects - Thematic Grants
• Start date: November 01, 2020
• End date: October 31, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Paulo Regis Caron Ruffino
• Grantee: Paulo Regis Caron Ruffino
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Pesquisadores principais: Pedro Jose Catuogno
• Associated researchers: Christian da Silva Rodrigues ; Christian Horacio Olivera ; Diego Sebastian Ledesma
• Associated scholarship(s): 24/09988-3 - Stochastic inhomogeneous Euler equations, BP.PD; 24/06348-3 - Mean filed limit for partial diferential equations with rough noise, BP.DD; 23/06514-8 - Theory of rough path and applications to stochastic equations., BP.MS; + associated scholarships 23/06709-3 - Stochastic hyperbolic equations, BP.PD; 23/05866-8 - Introduction to derivative pricing in discrete time, BP.IC; 22/13413-0 - Decomposition of flows in averaging principles and stochastic transport equation, BP.PD; 22/06128-8 - Introduction to stochastic differential equations, BP.IC; 22/00176-0 - Assymptotic behavior of stochastic evolutionary equações, BP.PD; 22/00284-8 - Geometry of foliations via foliated Brownian motion, BP.DD - associated scholarships

Abstract

Our research group in Mathematics Department -- UNICAMP focus on the study of intertwined properties of stochastic analysis, geometry and dynamical systems, mainly concerning the theory of continuous time semimartingales (e.g., Brownian motion), and more recently including jumps (e.g., Lévy processes). This project, which connects researchers who use common techniques on probability and ergodic theory is centred on the following items: stochastic dynamics on manifolds (bifurcation of Markov processes via $n$-point processes), properties of certain SPDEs, rough path theory, diffusions on foliated spaces, decomposition of stochastic flows (and its applications in dynamics and geometry of associated bundles), dynamics of measures. The project is guided mainly by the following actions: i) support the orientation of masters and PhDs/researchers; ii) improve further the national and international scientific connections, with a continuous flow of top researchers coming to visit the group, or members of the group going to congresses, visiting collaborators and centres of top reputation in the area. (AU)

Scientific publications

(9)

(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)

OLIVERA, CHRISTIAN; LONDONO, JUAN D.. Euler-Lagrangian Approach to Stochastic Euler Equations in Sobolev Spaces. Journal of Mathematical Fluid Mechanics, v. 25, n. 3, p. 10-pg., 2023-08-01. (20/15691-2, 20/04426-6)

NEVES, WLADIMIR; OLIVERA, CHRISTIAN. Stochastic Transport Equations with Unbounded Divergence. JOURNAL OF NONLINEAR SCIENCE, v. 32, n. 4, p. 19-pg., 2022-08-01. (20/15691-2, 20/04426-6)

DA COSTA, PAULO HENRIQUE; HOGELE, MICHAEL A.; RUFFINO, PAULO R.. Stochastic n-point D-bifurcations of stochastic Levy flows and their complexity on finite spaces. Stochastics and Dynamics, v. 22, n. 07, p. 39-pg., 2022-05-10. (15/50122-0, 20/04426-6)

LIMA, LOURIVAL; RUFFINO, PAULO; SOUZA, FRANCYS. Stochastic near-optimal control: additive, multiplicative, non-Markovian and applications. European Physical Journal-Special Topics, v. 230, n. 14-15, p. 2783-2792, OCT 2021. (17/23003-6, 20/04426-6, 15/50122-0)

LIMA, LOURIVAL; RUFFINO, PAULO; SOUZA, FRANCYS. Stochastic near-optimal control: additive, multiplicative, non-Markovian and applications. European Physical Journal-Special Topics, JUN 2021. (15/50122-0, 17/23003-6, 20/04426-6)

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)

OLIVERA, CHRISTIAN; RICHARD, ALEXANDRE; TOMASEVIC, MILICA. Quantitative particle approximation of nonlinear Fokker-Planck equations with singular kernel. ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE, v. 24, n. 2, p. 59-pg., 2023-01-01. (20/15691-2, 20/04426-6)

POSSOBON, RENATA; RODRIGUES, CHRISTIAN S.. Geometric properties of disintegration of measures. Ergodic Theory and Dynamical Systems, v. N/A, p. 30-pg., 2024-10-11. (18/05309-3, 20/04426-6, 18/13481-0, 19/14724-7, 16/00332-1)

OLIVERA, CHRISTIAN; TUDOR, CIPRIAN A.. Absolute continuity of the solution to the stochastic Burgers equation. CHAOS SOLITONS & FRACTALS, v. 153, n. 2, DEC 2021. (20/15691-2, 20/04426-6)