Stochastic n-point D-bifurcations of stochastic Levy flows and their complexity on finite spaces

Autor(es)

Da Costa, Paulo Henrique ; Hogele, Michael A. ; Ruffino, Paulo R.

• Tipo de documento: Artigo Científico
• Fonte: Stochastics and Dynamics; v. 22, n. 07, p. 39-pg., 2022-05-10.

Resumo

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)

• Processo FAPESP: 15/50122-0 - Fenômenos dinâmicos em redes complexas: fundamentos e aplicações
• Beneficiário: Elbert Einstein Nehrer Macau
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 20/04426-6 - Dinâmica estocástica: aspectos analíticos, geométricos e aplicações
• Beneficiário: Paulo Regis Caron Ruffino
• Modalidade de apoio: Auxílio à Pesquisa - Temático