| Full text | |
| Author(s): |
Da Costa, Paulo Henrique
;
Hogele, Michael A.
;
Ruffino, Paulo R.
Total Authors: 3
|
| Document type: | Journal article |
| Source: | Stochastics and Dynamics; v. 22, n. 07, p. 39-pg., 2022-05-10. |
| Abstract | |
This paper refines the classical notion of a stochastic D-bifurcation to the respective family of n-point motions for homogeneous Markovian stochastic semiflows, such as stochastic Brownian flows of homeomorphisms, and their generalizations. This notion essentially detects at which level the support of the invariant measure of the k-point bifurcation has more than one connected component. Stochastic Brownian flows and their invariant measures were shown by Kunita (1990) to be rigid, in the sense of being uniquely determined by the 1-and 2-point motions. Ilene, only stochastic n-point bifurcation of level n = 1 or n = 2 can occur. For general homogeneous stochastic Markov semiflows this turns out to be false. This paper constructs minimal examples of where this rigidity is false in general on finite space and studies the complexity of the resulting n-point bifurcations. (AU) | |
| FAPESP's process: | 15/50122-0 - Dynamic phenomena in complex networks: basics and applications |
| Grantee: | Elbert Einstein Nehrer Macau |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 20/04426-6 - Stochastic dynamics: analytical and geometrical aspects with applications |
| Grantee: | Paulo Regis Caron Ruffino |
| Support Opportunities: | Research Projects - Thematic Grants |