Results 81 to 90 of about 92,426 (217)
Testing covariance separability for continuous functional data
Journal of Time Series Analysis, Volume 46, Issue 3, Page 402-420, May 2025.Analyzing the covariance structure of data is a fundamental task of statistics. While this task is simple for low‐dimensional observations, it becomes challenging for more intricate objects, such as multi‐variate functions. Here, the covariance can be so complex that just saving a non‐parametric estimate is impractical and structural assumptions are ...
Holger Dette +2 more
wiley +1 more source
Vitali properties of Banach analytic manifolds [PDF]
arXiv, 2016 We discuss possible generalizations of Vitali convergence theorem when the source and the target are Banach analytic manifolds. These results are then applied to study behavior of holomorphic mappings between Banach analytic manifolds. Explicit examples of manifolds having Vitali properties are also provided.
arxiv
Center manifolds and contractions on a scale of Banach spaces
Journal of Functional Analysis, 1987 AbstractWe give a new proof for the existence of a Ck-center manifold at a nonhyperbolic equilibrium point of a finite-dimensional vector field of class Ck. The problem is reduced to a fixed point problem on a scale of Banach spaces; these Banach spaces consist of mappings with a certain maximal exponential growth at infinity.
S. A. van Gils, André Vanderbauwhede
openaire +2 more sources
The Granger–Johansen representation theorem for integrated time series on Banach space
Journal of Time Series Analysis, Volume 46, Issue 3, Page 432-457, May 2025.We prove an extended Granger–Johansen representation theorem (GJRT) for finite‐ or infinite‐order integrated autoregressive time series on Banach space. We assume only that the resolvent of the autoregressive polynomial for the series is analytic on and inside the unit circle except for an isolated singularity at unity.
Phil Howlett +4 more
wiley +1 more source
Journal of Time Series Analysis, Volume 46, Issue 3, Page 582-595, May 2025.Estimating parameters of functional ARMA, GARCH and invertible processes requires estimating lagged covariance and cross‐covariance operators of Cartesian product Hilbert space‐valued processes. Asymptotic results have been derived in recent years, either less generally or under a strict condition.
Sebastian Kühnert
wiley +1 more source
On Darboux Theorem for symplectic forms on direct limits of symplectic Banach manifolds [PDF]
, 2018 Given an ascending sequence of weak symplectic Banach manifolds on which the Darboux theorem is true, we can ask about conditions under which the Darboux Theorem is also true on the direct limit. We will show in general, without very strong conditions, the answer is negative.
arxiv +1 more source
Mean‐field limit of non‐exchangeable systems
Communications on Pure and Applied Mathematics, Volume 78, Issue 4, Page 651-741, April 2025.Abstract This paper deals with the derivation of the mean‐field limit for multi‐agent systems on a large class of sparse graphs. More specifically, the case of non‐exchangeable multi‐agent systems consisting of non‐identical agents is addressed. The analysis does not only involve PDEs and stochastic analysis but also graph theory through a new concept ...
Pierre‐Emmanuel Jabin +2 more
wiley +1 more source
Manifolds of continuous BV-functions and vector measure regularity of Banach-Lie groups [PDF]
Geometric mechanics 2025We construct a smooth Banach manifold BV$([a,b], M)$ whose elements are suitably-defined functions $f:[a,b] \rightarrow M$ of bounded variation with values in a smooth Banach manifold $M$ which admits a local addition. If the target manifold is a Banach-Lie group $G$, with Lie algebra $\mathfrak{g}$, we obtain a Banach-Lie group BV$([a,b], G)$ with Lie
arxiv +1 more source
Differential Geometry and its Applications, 2019 Let $M$ be a closed manifold and let $N$ be a connected manifold without boundary. For each $k\in\mathbb{N}$ the set of $k$ times continuously differentiable maps between $M$ and $N$ has the structure of a smooth Banach manifold where the underlying manifold topology is the compact-open $C^k$ topology.
openaire +3 more sources
Foundations of Ghost Stability
Fortschritte der Physik, Volume 73, Issue 4, April 2025.Abstract The authors present a new method to analytically prove global stability in ghost‐ridden dynamical systems. The proposal encompasses all prior results and consequentially extends them. In particular, it is shown that stability can follow from a conserved quantity that is unbounded from below, contrary to expectation.
Verónica Errasti Díez +2 more
wiley +1 more source