| Full text | |
| 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, p. 10-pg., 2016-11-01. |
| 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: | 15/07278-0 - Stochastic dynamics: analytical and geometrical aspects with applications |
| Grantee: | Paulo Regis Caron Ruffino |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 12/18780-0 - Geometry of control systems, dynamical and stochastics systems |
| Grantee: | Marco Antônio Teixeira |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 11/14797-2 - Stochastic dynamics in foliated spaces |
| Grantee: | Leandro Batista Morgado |
| Support Opportunities: | Scholarships in Brazil - Doctorate (Direct) |
| FAPESP's process: | 11/50151-0 - Dynamical phenomena in complex networks: fundamentals and applications |
| Grantee: | Elbert Einstein Nehrer Macau |
| Support Opportunities: | Research Projects - Thematic Grants |