Research Grants 15/07278-0 - Dinâmica estocástica, Teoria ergódica - BV FAPESP
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Stochastic dynamics: analytical and geometrical aspects with applications

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)

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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)
LEDESMA, DIEGO S.. A local solution to the Navier?Stokes equations on manifolds via stochastic representation ?. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, v. 198, . (15/07278-0, 18/13481-0)
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, . (15/07278-0, 15/04723-2)
LEDESMA, DIEGO SEBASTIAN; DA SILVA, FABIANO BORGES. Invariance of 0-currents under diffusions. Stochastics and Dynamics, v. 17, n. 2, . (15/07278-0)
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, . (15/07278-0, 17/17670-0)
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, . (15/07278-0, 15/04723-2)
RUFFINO, PAULO R.. Exploring a Fourier-Malliavin numerical model. SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, v. 11, n. 1, p. 125-132, . (11/50151-0, 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, . (15/07278-0, 17/17670-0)
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, . (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., . (17/17670-0, 15/07278-0)
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, . (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, . (15/07278-0)
NEVES, WLADIMIR; OLIVERA, CHRISTIAN. Initial-boundary value problem for stochastic transport equations. STOCHASTICS AND PARTIAL DIFFERENTIAL EQUATIONS-ANALYSIS AND COMPUTATIONS, . (13/15795-9, 15/07278-0, 17/17670-0)
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, . (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, . (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, . (15/07278-0, 15/04723-2)
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, . (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, . (15/07278-0, 17/17670-0)
LEDESMA, DIEGO S.. Stochastic calculus on Frechet spaces. ADVANCES IN OPERATOR THEORY, v. 6, n. 1, . (18/13481-0, 15/07278-0)
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, . (15/07278-0, 18/16568-0, 12/18780-0)
OLIVERA, CHRISTIAN; SHAMAROVA, EVELINA. Gaussian density estimates for solutions of fully coupled forward-backward SDEs. Mathematische Nachrichten, v. 293, n. 8, p. 1554-1564, . (17/17670-0, 15/07278-0)
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, . (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, . (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, . (15/07278-0, 15/04723-2)
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, . (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, . (15/07278-0, 11/50151-0)
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., . (15/07278-0, 18/16568-0, 12/18780-0)
OLIVERA, CHRISTIAN. Probabilistic representation for mild solution of the Navier-Stokes equations. MATHEMATICAL RESEARCH LETTERS, v. 28, n. 2, p. 563-573, . (15/07278-0, 17/17670-0)
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., . (17/17670-0, 15/07278-0)
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., . (15/07278-0, 12/18780-0, 11/14797-2, 11/50151-0)