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Related papers: Affine Rough Models

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Several classes of *-algebras associated to the action of an affine transformation are considered, and an investigation of the interplay between the different classes of algebras is initiated. Connections are established that relate…

Mathematical Physics · Physics 2009-03-16 Joakim Arnlind , Sergei Silvestrov

In affine formation control problems, the construction of the framework with universal rigidity and affine localizability is a critical prerequisite, but it has not yet been well addressed, especially when additional agents join the…

Systems and Control · Electrical Eng. & Systems 2025-06-05 Huiming Li , Hao Chen , Xiangke Wang , Zhongkui Li , Lincheng Shen

In the present paper we investigate the mechanics of systems of affinely-rigid bodies, i.e., bodies rigid in the sense of affine geometry. Certain physical applications are possible in modelling of molecular crystals, granular media, and…

The class of affine LIBOR models is appealing since it satisfies three central requirements of interest rate modeling. It is arbitrage-free, interest rates are nonnegative and caplet and swaption prices can be calculated analytically. In…

Pricing of Securities · Quantitative Finance 2015-03-04 Stefan Waldenberger , Wolfgang Müller

We derive an explicit asymptotic approximation for the implied volatilities of Call options written on bonds assuming the short-rate is described by an affine short-rate model. For specific affine short-rate models, we perform numerical…

Mathematical Finance · Quantitative Finance 2021-06-09 Matthew Lorig , Natchanon Suaysom

We consider practical aspects of reconstructing planar curves with prescribed Euclidean or affine curvatures. These curvatures are invariant under the special Euclidean group and the equi-affine groups, respectively, and play an important…

Differential Geometry · Mathematics 2024-04-02 Jose Agudelo , Brooke Dippold , Ian Klein , Alex Kokot , Eric Geiger , Irina Kogan

This paper aims to develop a theory of projective and affine structures on higher-dimensional varieties in positive characteristic. This theory deals with Frobenius-projective and Frobenius-affine structures, which have been previously…

Algebraic Geometry · Mathematics 2026-05-19 Yasuhiro Wakabayashi

Our goal is to provide a review of deep learning methods which provide insight into structured high-dimensional data. Rather than using shallow additive architectures common to most statistical models, deep learning uses layers of…

Machine Learning · Statistics 2023-10-11 Nick Polson , Vadim Sokolov

This work sets the statistical affine shape theory in the context of real normed division algebras. The general densities apply for every field: real, complex, quaternion, octonion, and for any noncentral and non-isotropic elliptical…

Statistics Theory · Mathematics 2010-12-30 Jose A. Diaz-Garcia , Francisco J. Caro-Lopera

We classify affine varieties with an action of a connected, reductive algebraic group such that the group is isomorphic to an open orbit in the variety. This is accomplished by associating a set of one-parameter subgroups of the group to…

Algebraic Geometry · Mathematics 2010-12-20 David Murphy

Models characterized by autoregressive structure and random coefficients are powerful tools for the analysis of high-frequency, high-dimensional and volatile time series. The available literature on such models is broad, but also sectorial,…

Methodology · Statistics 2020-09-18 Marta Regis , Paulo Serra , Edwin R. van den Heuvel

The long-ranged elastic model, which is believed to describe the evolution of a self-affine rough crack-front, is analyzed to linear and non-linear orders. It is shown that the nonlinear terms, while important in changing the front…

Disordered Systems and Neural Networks · Physics 2009-11-13 Eran Bouchbinder , Michal Bregman , Itamar Procaccia

The main aim of the paper is to formulate and prove a result about the structure of double affine Hecke algebras which allows its two commutative subalgebras to play a symmetric role. This result is essential for the theory of intertwiners…

Quantum Algebra · Mathematics 2007-05-23 Bogdan Ion

We introduce the notion of affine strict polynomial functor. We show how this concept helps to understand homological behavior of the operation of Frobenius twist in the category of strict polynomial functors over a field of positive…

K-Theory and Homology · Mathematics 2014-11-14 Marcin Chałupnik

A new paradigm recently emerged in financial modelling: rough (stochastic) volatility, first observed by Gatheral et al. in high-frequency data, subsequently derived within market microstructure models, also turned out to capture…

Pricing of Securities · Quantitative Finance 2017-10-23 Christian Bayer , Peter K. Friz , Paul Gassiat , Joerg Martin , Benjamin Stemper

In a recent paper it was proposed that for some nonlinear shell models of turbulence one can construct a linear advection model for an auxiliary field such that the scaling exponents of all the structure functions of the linear and…

Chaotic Dynamics · Physics 2009-11-11 Roberto Benzi , Boris Levant , Itamar Procaccia , Edriss S. Titi

Ext-int.\ one affine functions are functions affine in the direction of one-divisible exterior forms, with respect to exterior product in one variable and with respect to interior product in the other. The purpose of this article is to…

Functional Analysis · Mathematics 2025-04-02 Saugata Bandyopadhyay , Swarnendu Sil

We introduce the notion of amenability for affine algebras. We characterize amenability by Folner-sequences, paradoxicality and the existence of finitely invariant dimension-measures. Then we extend the results of Rowen on ranks, from…

Rings and Algebras · Mathematics 2007-05-23 Gabor Elek

Some time ago, conformal data with affine fusion rules were found. Our purpose here is to realize some of these conformal data, using systems of free bosons and parafermions. The so constructed theories have an extended $W$ algebras which…

High Energy Physics - Theory · Physics 2009-10-31 Doron Gepner

This paper is concerned with finite dimensional models for the entire term structure for energy futures. As soon as a finite dimensional set of possible yield curves is chosen, one likes to estimate the dynamic behaviour of the yield curve…

Mathematical Finance · Quantitative Finance 2023-08-07 Paul Krühner , Shijie Xu