Decomposition of stochastic flows with automorphism of subbundles component

We show that given a $G$-structure $P$ on a differentiable manifold $M$, if the group $G(M)$ of automorphisms of $P$ is big enough, then there exists the quotient of an stochastic flows $phi_t$ by $G(M)$, in the sense that $\phi_t = \xi_t \circ \rho_t$ where $\xi_t \in G(M)$, the remainder $\rho_t$ has derivative which is vertical but transversal to the fibre of $P$. This geometrical context generalizes previous results where $M$ is a Riemannian manifold and $\phi_t$ is decomposed with an isometric component, see Liao \cite{Liao1} and Ruffino \cite{Ruffino}, which in our context corresponds to the particular case of an SO(n)-structure on $M$.Comment: To appear in Stochastics and Dynamics, 201

Weak solutions for stochastic differential equations with additive fractional noise

We give a new approach to prove the existence of a weak solution of $$dx_t = f(t,x_t)dt + g(t)dB^H_t$$ where $B^H_t$ is a fractional Brownian motion with values in a separable Hilbert space for suitable functions $f$ and $g$. Our idea is to use the implicit function theorem and the scaling property of the fractional Brownian motion in order to obtain a weak solution for this equation.Comment: 10page

Foliated Stochastic Calculus: Harmonic Measures

FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOIn this article we present an intrinsic construction of foliated Brownian motion (FoBM) via stochastic calculus adapted to a foliated Riemannian manifold (M, F). The stochastic approach together with this proposed foliated vector calculus provide a natural method to work with (L. Garnett's) harmonic measures in M. New results include, beside an explicit stochastic equation for the FoBM, a decomposition of the Laplacian of M in terms of the foliated and the basic Laplacians, a characterization of totally invariant measures and a differential equation for the density of harmonic measures.In this article we present an intrinsic construction of foliated Brownian motion (FoBM) via stochastic calculus adapted to a foliated Riemannian manifold (M, F). The stochastic approach together with this proposed foliated vector calculus provide a natural method to work with (L. Garnett's) harmonic measures in M. New results include, beside an explicit stochastic equation for the FoBM, a decomposition of the Laplacian of M in terms of the foliated and the basic Laplacians, a characterization of totally invariant measures and a differential equation for the density of harmonic measures.3681563579FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOFAPESP [11/50151-0, 12/18780-0]11/50151-0; 12/18780-

Representation of the Santander Cathedral by Combination of Different Smart Techniques

Inside Santander city, we find two different historical parts, ''la Puebla vieja'', oldest part of the city, where the cathedral is located and ''la Puebla nueva''. A research team has been created with two purposes: study and make the architectural survey of historic building, through collaboration between the emerged company, 3D Intelligence, the Universidad de Cantabria, the Universit degli Studi di Napoli ''Federico II'' and the School - Workshop from the City Council of Santander, thus a number of projects for the digital documentation of the Santander City Heritage have been generated [1] as the beginning of the analysis and three-dimensional modeling of the historical evolution of the city. For which we used a new methodology for understanding the Historic Urban Landscape [2], trying to validate the novel concepts in the field of cultural heritage [3