Stochastic dynamics in foliated spaces

• Grant number: 11/14797-2
• Support Opportunities: Scholarships in Brazil - Doctorate (Direct)
• Start date: March 01, 2012
• End date: May 31, 2015
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Paulo Regis Caron Ruffino
• Grantee: Leandro Batista Morgado
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 07/06896-5 - Geometry of control, dynamical and stochastic systems, AP.TEM

Abstract

This project concerns the education of a researcher on stochastic geometry and dynamics, more precisely on diffusions in a foliated space. In this area, the two main problems to focus the research are: 1) in a principal fibre bundle, to establish the dependence on the connection of the decomposition of stochastic flows according to complementary distributions (horizontal and vertical), extending previous results of the supervisor and collaborators (Stochastics and Dynamics, 2011); 2) To develop a theory of measurable flows in foliated spaces, mainly inspired by the coalescence flows as in LeJan e Raymond (Annals Prob. 2004) . (AU)

Scientific publications

(4)

(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)

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)

MELO, ALISON M.; MORGADO, LEANDRO; RUFFINO, PAULO R.. Topology of Foliations and Decomposition of Stochastic Flows of Diffeomorphisms. Journal of Dynamics and Differential Equations, v. 30, n. 1, p. 39-54, MAR 2018. (11/50151-0, 11/14797-2, 12/18780-0)

MORGADO, LEANDRO; RUFFINO, PAULO R.. Extension of time for decomposition of stochastic flows in spaces with complementary foliations. Electronic Communications in Probability, v. 20, p. 1-9, MAY 17 2015. (12/18780-0, 11/14797-2, 11/50151-0)

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)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

MORGADO, Leandro Batista. Dynamics of semimartingales with jumps: decomposition and delay. 2015. Doctoral Thesis - Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica Campinas, SP.