Results 31 to 40 of about 23,971 (153)
, 2019 The manifold structure of subsets of classical probability distributions and quantum density operators in infinite dimensions is investigated in the context of $C^{*}$-algebras and actions of Banach-Lie groups.
Ciaglia, Florio M. +3 more
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Rough PDEs for Local Stochastic Volatility Models
Mathematical Finance, EarlyView.ABSTRACT In this work, we introduce a novel pricing methodology in general, possibly non‐Markovian local stochastic volatility (LSV) models. We observe that by conditioning the LSV dynamics on the Brownian motion that drives the volatility, one obtains a time‐inhomogeneous Markov process. Using tools from rough path theory, we describe how to precisely
Peter Bank +3 more
wiley +1 more source
On an Erdős similarity problem in the large
Bulletin of the London Mathematical Society, EarlyView.Abstract In a recent paper, Kolountzakis and Papageorgiou ask if for every ε∈(0,1]$\epsilon \in (0,1]$, there exists a set S⊆R$S \subseteq \mathbb {R}$ such that |S∩I|⩾1−ε$\vert S \cap I\vert \geqslant 1 - \epsilon$ for every interval I⊂R$I \subset \mathbb {R}$ with unit length, but that does not contain any affine copy of a given increasing sequence ...
Xiang Gao +2 more
wiley +1 more source
Lusternik-Schnirelman theory on Banach manifolds [PDF]
Topology, 1966 SEVERAL years ago the author, and independently Smale, generalized the Morse theory of critical points to cover certain functions on hilbert manifolds [5,6 and 91. Shortly thereafter J. Schwartz showed how the same techniques allowed one also to extend the LusternikSchnirelman theory of critical points to functions on hilbert manifolds [7].
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The small‐scale limit of magnitude and the one‐point property
Bulletin of the London Mathematical Society, EarlyView.Abstract The magnitude of a metric space is a real‐valued function whose parameter controls the scale of the metric. A metric space is said to have the one‐point property if its magnitude converges to 1 as the space is scaled down to a point. Not every finite metric space has the one‐point property: to date, exactly one example has been found of a ...
Emily Roff, Masahiko Yoshinaga
wiley +1 more source
Graphical models for topological groups: A case study on countable Stone spaces
Bulletin of the London Mathematical Society, EarlyView.Abstract By analogy with the Cayley graph of a group with respect to a finite generating set or the Cayley–Abels graph of a totally disconnected, locally compact group, we detail countable connected graphs associated to Polish groups that we term Cayley–Abels–Rosendal graphs.
Beth Branman +3 more
wiley +1 more source
Induction for weak symplectic Banach manifolds
Journal of Geometry and Physics, 2008 The symplectic induction procedure is extended to the case of weak symplectic Banach manifolds. Using this procedure, one constructs hierarchies of integrable Hamiltonian systems related to the Banach Lie‐Poisson spaces of k-diagonal trace class operators.
Odzijewicz, Anatol, Ratiu, Tudor S.
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Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.Abstract We study convergence problems for the intermediate long wave (ILW) equation, with the depth parameter δ>0$\delta > 0$, in the deep‐water limit (δ→∞$\delta \rightarrow \infty$) and the shallow‐water limit (δ→0$\delta \rightarrow 0$) from a statistical point of view.
Guopeng Li, Tadahiro Oh, Guangqu Zheng
wiley +1 more source
The Banach manifold structure of the space of metrics on noncompact manifolds
Differential Geometry and its Applications, 1991 AbstractWe study the Ck-structure of the space of Riemannian metrics of bouded geometry on open manifolds, the group of bounded diffeomorphisms, its action and the factor space. Each component of the space of metrics has a natural Banach manifold structure and the group of bounded diffeomorphisms is a completely metrizable topological group.
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Sub-Riemannian Geometry and Geodesics in Banach Manifolds [PDF]
The Journal of Geometric Analysis, 2019 In this paper, we define and study sub-Riemannian structures on Banach manifolds. We obtain extensions of the Chow-Rashevski theorem for exact controllability, and give conditions for the existence of a Hamiltonian geodesic flow despite the lack of a Pontryagin Maximum Principle in the infinite dimensional setting.
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