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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Extension of time for decomposition of stochastic flows in spaces with complementary foliations

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Author(s):
Morgado, Leandro [1] ; Ruffino, Paulo R. [1]
Total Authors: 2
Affiliation:
[1] Univ Estadual Campinas, Dept Matemat, BR-13081970 Campinas, SP - Brazil
Total Affiliations: 1
Document type: Journal article
Source: Electronic Communications in Probability; v. 20, p. 1-9, MAY 17 2015.
Web of Science Citations: 1
Abstract

Let M be a manifold equipped (locally) with a pair of complementary foliations. In Catuogno, da Silva and Ruffino {[}4], it is shown that, up to a stopping time tau, a stochastic flow of local diffeomorphisms phi(t) in M can be decomposed in diffeomorphisms that preserves this foliations. In this article we present techniques which allow us to extend the time of this decomposition. For this extension, we use two techniques: In the first one, assuming that the vector fields of the system commute with each other, we apply Marcus equation to jump nondecomposable diffeomorphisms. The second approach deals with the general case: we introduce a `stop and go' technique that allows us to construct a process that follows the original flow in the `good zones' for the decomposition, and remains paused in `bad zones'. Among other applications, our results open the possibility of studying the asymptotic behaviour of each component. (AU)

FAPESP's process: 11/50151-0 - Dynamical phenomena in complex networks: fundamentals and applications
Grantee:Elbert Einstein Nehrer Macau
Support type: Research Projects - Thematic Grants
FAPESP's process: 11/14797-2 - Stochastic dynamics in foliated spaces
Grantee:Leandro Batista Morgado
Support type: Scholarships in Brazil - Doctorate (Direct)
FAPESP's process: 12/18780-0 - Geometry of control systems, dynamical and stochastics systems
Grantee:Marco Antônio Teixeira
Support type: Research Projects - Thematic Grants