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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.)

DECOMPOSITION OF STOCHASTIC FLOWS GENERATED BY STRATONOVICH SDES WITH JUMPS

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Author(s):
Melo, Alison M. ; Morgado, Leandro B. ; Ruffino, Paulo R.
Total Authors: 3
Document type: Journal article
Source: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B; v. 21, n. 9, SI, p. 3209-3218, NOV 2016.
Web of Science Citations: 0
Abstract

Consider a manifold M endowed locally with a pair of complementary distributions Delta(H) (R) Delta(V) = TM and let Diff(Delta(H), M) and Diff(Delta(V), M) be the corresponding Lie subgroups generated by vector fields in the corresponding distributions. We decompose a stochastic flow with jumps, up to a stopping time, as phi(t) = xi(t) o psi(t), where xi(t) is an element of Diff(Delta(H), M) and psi(t) is an element of Diff(Delta(V), M). Our main result provides Stratonovich stochastic differential equations with jumps for each of these two components in the corresponding infinite dimensional Lie groups. We present an extension of the It (o) over cap -Ventzel-Kunita formula for stochastic flows with jumps generated by classical Marcus equation (as in Kurtz, Pardoux and Protter {[}11]). The results here correspond to an extension of Catuogno, da Silva and Ruffino {[}4], where this decomposition was studied for the continuous case. (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: 15/07278-0 - Stochastic dynamics: analytical and geometrical aspects with applications
Grantee:Paulo Regis Caron Ruffino
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