Stochastic dynamics: analytical and geometrical aspects with applications

• Grant number: 15/07278-0
• Support Opportunities: Research Projects - Thematic Grants
• Duration: February 01, 2016 - January 31, 2020
• 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 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

(29)

(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)

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. (15/07278-0, 15/04723-2)

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. (15/07278-0, 15/04723-2)

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. (15/07278-0, 17/17670-0)

LEDESMA, DIEGO SEBASTIAN; DA SILVA, FABIANO BORGES. Invariance of 0-currents under diffusions. Stochastics and Dynamics, v. 17, n. 2, APR 2017. (15/07278-0)

OLIVERA, CHRISTIAN. Well-posedness of the non-local conservation law by stochastic perturbation. MANUSCRIPTA MATHEMATICA, v. 162, n. 3-4, p. 367-387, JUL 2020. (15/07278-0, 17/17670-0)

LEDESMA, DIEGO S.. A local solution to the Navier?Stokes equations on manifolds via stochastic representation ?. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, v. 198, SEP 2020. (15/07278-0, 18/13481-0)

RUFFINO, PAULO R.. Exploring a Fourier-Malliavin numerical model. SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, v. 11, n. 1, p. 125-132, JUN 2017. (11/50151-0, 15/07278-0)

NEVES, WLADIMIR; OLIVERA, CHRISTIAN. Initial-boundary value problem for stochastic transport equations. STOCHASTICS AND PARTIAL DIFFERENTIAL EQUATIONS-ANALYSIS AND COMPUTATIONS, v. 9, n. 3, p. 674-701, SEP 2021. (15/07278-0, 17/17670-0, 13/15795-9)

OLIVERA, CHRISTIAN; SHAMAROVA, EVELINA. Gaussian density estimates for solutions of fully coupled forward-backward SDEs. Mathematische Nachrichten, v. 293, n. 8, p. 11-pg., 2020-05-25. (17/17670-0, 15/07278-0)

CLARKE, JORGE; OLIVERA, CHRISTIAN. LOCAL L-p-SOLUTION FOR SEMILINEAR HEAT EQUATION WITH FRACTIONAL NOISE. ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, v. 45, p. 305-312, 2020. (15/07278-0, 17/17670-0)

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. (15/07278-0, 17/17670-0)

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. (15/07278-0, 17/17670-0)

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. (15/07278-0, 15/04723-2)

LEDESMA, DIEGO SEBASTIAN; BORGES DA SILVA, FABIANO. Decomposition of stochastic flow and an averaging principle for slow perturbations. DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, v. 35, n. 4, p. 625-654, OCT 1 2020. (15/07278-0, 18/16568-0, 12/18780-0)

NEVES, WLADIMIR; OLIVERA, CHRISTIAN. Initial-boundary value problem for stochastic transport equations. STOCHASTICS AND PARTIAL DIFFERENTIAL EQUATIONS-ANALYSIS AND COMPUTATIONS, SEP 2020. (13/15795-9, 15/07278-0, 17/17670-0)

LEDESMA, DIEGO SEBASTIAN; ANAYA, ROBERT ANDRES GALEANO; BORGES DA SILVA, FABIANO. Estimates for the volume variation of compact submanifolds driven by a stochastic flow. DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, v. N/A, p. 27-pg., 2022-06-07. (15/07278-0, 18/16568-0, 12/18780-0)

DE LA CRUZ, H.; OLIVERA, C.. An explicit numerical scheme for the computer simulation of the stochastic transport equation. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, v. 110, p. 14-pg., 2022-07-01. (17/17670-0, 15/07278-0)

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. (15/07278-0, 17/17670-0)

CATUOGNO, PEDRO J.; LEDESMA, DIEGO S.; RUFFINO, PAULO R.. Harmonic measures in embedded foliated manifolds. Stochastics and Dynamics, v. 17, n. 4, AUG 2017. (15/07278-0, 11/50151-0)

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. (15/07278-0, 12/18780-0, 18/16568-0)

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. (15/07278-0, 12/18940-7, 15/04723-2)

CATUOGNO, PEDRO; MOLINA, SANDRA; OLIVERA, C.. Generalized functions and Laguerre expansions. MONATSHEFTE FUR MATHEMATIK, v. 184, n. 1, p. 51-75, SEP 2017. (15/07278-0, 15/04723-2)

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. (11/50151-0, 15/07278-0, 11/14797-2, 12/18780-0)

OLIVERA, CHRISTIAN; SHAMAROVA, EVELINA. Gaussian density estimates for solutions of fully coupled forward-backward SDEs. Mathematische Nachrichten, v. 293, n. 8, MAY 2020. (15/07278-0)

OLIVERA, CHRISTIAN. Probabilistic representation for mild solution of the Navier-Stokes equations. MATHEMATICAL RESEARCH LETTERS, v. 28, n. 2, p. 563-573, 2021. (15/07278-0, 17/17670-0)

LEDESMA, DIEGO S.. Stochastic calculus on Frechet spaces. ADVANCES IN OPERATOR THEORY, v. 6, n. 1, JAN 2021. (18/13481-0, 15/07278-0)

OLIVERA, CHRISTIAN; SHAMAROVA, EVELINA. Gaussian density estimates for solutions of fully coupled forward-backward SDEs. Mathematische Nachrichten, v. 293, n. 8, p. 1554-1564, AUG 2020. (17/17670-0, 15/07278-0)

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. (15/07278-0, 17/17670-0)

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, p. 10-pg., 2016-11-01. (15/07278-0, 12/18780-0, 11/14797-2, 11/50151-0)