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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)
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)
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)
LEDESMA, DIEGO SEBASTIAN; DA SILVA, FABIANO BORGES. Invariance of 0-currents under diffusions. Stochastics and Dynamics, v. 17, n. 2, . (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)
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)
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; 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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
LEDESMA, DIEGO S.. Stochastic calculus on Frechet spaces. ADVANCES IN OPERATOR THEORY, v. 6, n. 1, . (18/13481-0, 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, . (15/07278-0, 17/17670-0)
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)
OLIVERA, CHRISTIAN; SHAMAROVA, EVELINA. Gaussian density estimates for solutions of fully coupled forward-backward SDEs. Mathematische Nachrichten, v. 293, n. 8, . (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)
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)
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)

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