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Stochastic dynamics: analytical and geometrical aspects with applications

Grant number: 15/07278-0
Support type:Research Projects - Thematic Grants
Duration: February 01, 2016 - January 31, 2020
Field of knowledge:Physical Sciences and Mathematics - Mathematics
Principal Investigator:Paulo Regis Caron Ruffino
Grantee:Paulo Regis Caron Ruffino
Home Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Co-Principal Investigators:Pedro Jose Catuogno
Assoc. researchers:Christian Horacio Olivera ; Diego Sebastian Ledesma ; Eduardo Garibaldi
Associated scholarship(s):18/06531-1 - Dynamical systems perturbed by Lévy processes, BP.PD
17/23003-6 - Functional stochastic analysis and applications, BP.PD
17/23932-7 - Introduction to control theory, BP.IC

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 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, diffusions on foliated spaces, decomposition of stochastic flows (and its applications in dynamics and geometry of associated bundles), coupled systems and equilibrium for cellular automata with memory. 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 (15)
(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)
LUQUE JUSTO, CLAUDIA; LEDESMA, DIEGO SEBASTIAN; SILVA, FABIANO BORGES. An isometric embedding of the g(t)-Brownian motion with application in stability and homotopy group. Stochastics and Dynamics, v. 19, n. 6 DEC 2019. Web of Science Citations: 0.
OLIVERA, CHRISTIAN; TUDOR, CIPRIAN. Density for solutions to stochastic differential equations with unbounded drift. BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS, v. 33, n. 3, p. 520-531, AUG 2019. Web of Science Citations: 0.
OLIVERA, CHRISTIAN; TUDOR, CIPRIAN A. Existence and Besov regularity of the density for a class of SDEs with Volterra noise. COMPTES RENDUS MATHEMATIQUE, v. 357, n. 7, p. 636-645, JUL 2019. Web of Science Citations: 0.
FERRARIO, BENEDETTA; OLIVERA, CHRISTIAN. 2D Navier-Stokes equation with cylindrical fractional Brownian noise. Annali di Matematica Pura ed Applicata, v. 198, n. 3, p. 1041-1067, JUN 2019. Web of Science Citations: 0.
MOLLINEDO, DAVID A. C.; OLIVERA, CHRISTIAN; TUDOR, CIPRIAN A. Existence and Smoothness of the Density for the Stochastic Continuity Equation. Results in Mathematics, v. 74, n. 1 MAR 2019. Web of Science Citations: 0.
SIMON, MARIELLE; OLIVERA, CHRISTIAN. Non-local Conservation Law from Stochastic Particle Systems. Journal of Dynamics and Differential Equations, v. 30, n. 4, p. 1661-1682, DEC 2018. Web of Science Citations: 0.
CATUOGNO, P.; COLOMBEAU, J. F.; OLIVERA, C. Generalized solutions of the multidimensional stochastic Burgers equation. Journal of Mathematical Analysis and Applications, v. 464, n. 2, p. 1375-1382, AUG 15 2018. Web of Science Citations: 1.
FERRARIO, BENEDETTA; OLIVERA, CHRISTIAN. L-p-solutions of the Navier-Stokes equation with fractional Brownian noise. AIMS MATHEMATICS, v. 3, n. 4, p. 539-553, 2018. Web of Science Citations: 0.
MOLLINEDO, DAVID A. C.; OLIVERA, CHRISTIAN. Well-Posedness of the Stochastic Transport Equation with Unbounded Drift. BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, v. 48, n. 4, p. 663-677, DEC 2017. Web of Science Citations: 0.
MOLLINEDO, DAVID A. C.; OLIVERA, CHRISTIAN. Stochastic continuity equation with nonsmooth velocity. Annali di Matematica Pura ed Applicata, v. 196, n. 5, p. 1669-1684, OCT 2017. Web of Science Citations: 3.
CATUOGNO, PEDRO; MOLINA, SANDRA; OLIVERA, C. Generalized functions and Laguerre expansions. MONATSHEFTE FUR MATHEMATIK, v. 184, n. 1, p. 51-75, SEP 2017. Web of Science Citations: 0.
CATUOGNO, PEDRO J.; LEDESMA, DIEGO S.; RUFFINO, PAULO R. Harmonic measures in embedded foliated manifolds. Stochastics and Dynamics, v. 17, n. 4 AUG 2017. Web of Science Citations: 0.
RUFFINO, PAULO R. Exploring a Fourier-Malliavin numerical model. SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, v. 11, n. 1, p. 125-132, JUN 2017. Web of Science Citations: 0.
LEDESMA, DIEGO SEBASTIAN; DA SILVA, FABIANO BORGES. Invariance of 0-currents under diffusions. Stochastics and Dynamics, v. 17, n. 2 APR 2017. Web of Science Citations: 0.
MELO, ALISON M.; MORGADO, LEANDRO B.; RUFFINO, PAULO R. DECOMPOSITION OF STOCHASTIC FLOWS GENERATED BY STRATONOVICH SDES WITH JUMPS. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, v. 21, n. 9, SI, p. 3209-3218, NOV 2016. Web of Science Citations: 0.

Please report errors in scientific publications list by writing to: cdi@fapesp.br.