arXiv research

This paper presents generalized momentum mappings for covariant Hamiltonian field theories. The new momentum mappings arise from a generalization of symplectic geometry to $L_VY$, the bundle of vertically adapted linear frames over the bundle of field configurations $Y$. Specifically, the generalized field momentum obs…

In this note, we study the ultimate ruin probabilities of a real-valued L{é}vy process X with light-tailed negative jumps. It is well-known that, for such L{é}vy processes, the probability of ruin decreases as an exponential function with a rate given by the root of the Laplace exponent, when the initial value goes to …

We prove that a compact stratied space satises the Riemannian curvature-dimension condition RCD(K, N) if and only if its Ricci tensor is bounded below by K $\in$ R on the regular set, the cone angle along the stratum of codimension two is smaller than or equal to 2$π$ and its dimension is at most equal to N. This gives…

This article is devoted to the maximisation of HARA utilities of L{é}vy switching process on finite time interval via dual method. We give the description of all f-divergence minimal martingale measures in initially enlarged filtration, the expression of their Radon-Nikodym densities involving Hellinger and Kulback-Lei…

In this paper, we study the ruin problem with investment in a general framework where the business part X is a L{é}vy process and the return on investment R is a semimartingale. We obtain upper bounds on the finite and infinite time ruin probabilities that decrease as a power function when the initial capital increases…

Let $M$ be a manifold, $V$ be a vector field on $M$, and $B$ be a Banach space. For any fixed function $f:M\rightarrow B$ and any fixed complex number $λ$, we study Hyers-Ulam stability of the global differential equation $Vy=λy+f$.

In this paper, we provide a representation theorem for dynamic capital allocation under It{ô}-L{é}vy model. We consider the representation of dynamic risk measures defined under Backward Stochastic Differential Equations (BSDE) with generators that grow quadratic-exponentially in the control variables. Dynamic capital …

The Wiener-Hopf factorization is obtained in closed form for a phase type approximation to the CGMY Lévy process. This allows, for the approximation, exact computation of first passage times to barrier levels via Laplace transform inversion. Calibration of the CGMY model to market option prices defines the risk neutral…

We introduce a class of interest rate models, called the $α$-CIR model, which gives a natural extension of the standard CIR model by adopting the $α$-stable L{é}vy process and preserving the branching property. This model allows to describe in a unified and parsimonious way several recent observations on the sovereign …

Many recent papers address reading comprehension, where examples consist of (question, passage, answer) tuples. Presumably, a model must combine information from both questions and passages to predict corresponding answers. However, despite intense interest in the topic, with hundreds of published papers vying for lead…

Constructs supermartingale couplings with full marginals constraints.

The distribution of trade sizes and trading volumes are investigated based on the limit order book data of 22 liquid Chinese stocks listed on the Shenzhen Stock Exchange in the whole year 2003. We observe that the size distribution of trades for individual stocks exhibits jumps, which is caused by the number preference…

Defines vector Laplacian on statistical manifolds.

We provide an empirical investigation aimed at uncovering the statistical properties of intricate stock trading networks based on the order flow data of a highly liquid stock (Shenzhen Development Bank) listed on Shenzhen Stock Exchange during the whole year of 2003. By reconstructing the limit order book, we can extra…

BIG Laplacians bridge combinatorial and Hodge Laplacians for discrete data.

Paper introduces magnetic Hodge Laplacian for differential forms.

The paper extends Laplacian spectra approximations to vector bundles.

Proves Laplacian and Lichnerowicz Laplacian are sectorial in weighted Hölder spaces.

Survey of Laplacian-based methods for data dimensionality reduction and embedding.

The graph Laplacian plays key roles in information processing of relational data, and has analogies with the Laplacian in differential geometry. In this paper, we generalize the analogy between graph Laplacian and differential geometry to the hypergraph setting, and propose a novel hypergraph $p$-Laplacian. Unlike the …

The paper sets up eigenvalue comparison theorems for specific Laplacians on manifolds.

Extended bounds on small eigenvalues for pseudo-Laplacians on hyperbolic surfaces.

Paper investigates rigidity phenomena for weighted Ricci curvature bounds with Laplacian comparison theorem.

Study Hodge Laplacians for manifold data, improving error bounds.

Root Laplacian Eigenmaps help in spectral embedding of graphs.

New perspective on G2-structures flow from DeTurck Laplacian.

A kinematic method selects the deformation Laplacian for fluid dynamics on Riemannian manifolds.

Study solves sub-Laplacian equivalence on a specific Heisenberg group.

Explains BV Laplacian on half-densities in simple terms.

Study shows rates for Laplacian-eigenmap methods in nonparametric regression.

Study eigenvalues of p-Laplacian on quaternionic Kähler manifolds.

The paper finds new inequalities for Laplacian and biharmonic eigenvalues on manifolds.

Researchers find second-order estimates for $p$-Laplacian in RCD spaces.

Study on $G_2$-structures using Laplacian coflow and solitons.

Study of Yang-Mills fields on 4-manifolds using modified Lévy Laplacians.

For a bounded domain $Ω$ with a piecewise smooth boundary in an $n$-dimensional Euclidean space $\mathbf{R}^{n}$, we study eigenvalues of the Dirichlet eigenvalue problem of the Laplacian. First we give a general inequality for eigenvalues of the Laplacian. As an application, we study lower order eigenvalues of the Lap…

Fractional Laplacian inverse problem solved for connection Laplacians.

New upper bound for Neumann Laplacian eigenvalues on convex domains.

Universal inequalities found for Laplacian eigenvalues on convex domains.

Universal inequalities for Laplacian eigenvalues on convex domains.

New inequalities for planar convex domains' Laplacian eigenvalues.

We investigate the existence of closed $G_2$-structures which are solitons for the Laplacian flow on nilpotent Lie groups. We obtain that seven of the twelve Lie algebras admitting a closed $G_2$-structure do admit a Laplacian soliton. Moreover, one of them admits a continuous family of Laplacian solitons which are pai…

New examples found for a type of geometric solitons.

New theorems compare Laplacian on Kähler manifolds.

The paper studies eigenfunctions and nodal sets of the Witten-Laplacian.

Maps commuting with sub-Laplacians on Carnot groups are conformal.

In this paper, we obtain "universal" inequalities for eigenvalues of the weighted Hodge Laplacian on a compact self-shrinker of Euclidean space. These inequalities generalize the Yang-type and Levitin-Parnovski inequalities for eigenvalues of the Laplacian and Laplacian. From the recursion formula of Cheng and Yang \ci…

Study on p-Laplacian problems with critical exponent, focusing on existence of solutions.