A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Random geodesics on curved surfaces form a pattern similar to random lines.
The telegraph process models a random motion with finite velocity and it is usually proposed as an alternative to diffusion models. The process describes the position of a particle moving on the real line, alternatively with constant velocity or . The changes of direction are governed by an homogeneous Poisso…
Modeling trading volume curves using hierarchical Poisson processes.
The paper constructs and generalizes Poisson brackets for Jacobi elliptic functions and higher-dimensional systems.
New algebraic framework for Jacobi manifolds connects geometric mechanics and dimensional analysis.
Study optimal asset allocation for insurers with multiple lines of business and constraints.
Given a compact oriented surface, we classify log Poisson bi-vectors whose degeneracy loci are locally modeled by a finite set of lines in the plane intersecting at a point. Further, we compute the Poisson cohomology of such structures and discuss the relationship between our classification and the second Poisson cohom…
This chapter is an attempt to present a mathematical theory of compound fractional Poisson processes. The chapter begins with the characterization of a well-known Lévy process: The compound Poisson process. The semi-Markov extension of the compound Poisson process naturally leads to the compound fractional Poisson proc…
Single linear solve combines surface reconstruction and uncertainty quantification.
We first extend the notion of connection in the context of Courant algebroids to obtain a new characterization of generalized Kaehler geometry. We then establish a new notion of isomorphism between holomorphic Poisson manifolds, which is non-holomorphic in nature. Finally we show an equivalence between certain configur…
We identify the cotangent bundle Lie algebroid of a Poisson homogeneous space G/H of a Poisson Lie group G as a quotient of a transformation Lie algebroid over G. As applications, we describe the modular vector fields of G/H, and we identify the Poisson cohomology of G/H with coefficients in powers of its canonical lin…
On an orientable manifold M, we consider a regular even dimensional foliation F which is globally defined by a set of k-independent 1-forms. We give necessary and sufficient conditions for the existence of a regular Poisson structure on M whose Characteristic foliation is precisely F. Moreover, introducing a special cl…
New model distinguishes Poisson processes from self-similar ones.
In this paper, we study the interplay between modules and sub-objects in holomorphic Poisson geometry. In particular, we define a new notion of "residue" for a Poisson module, analogous to the Poincaré residue of a meromorphic volume form. Of particular interest is the interaction between the residues of the canonical …
We show that the stick-breaking construction of the beta process due to Paisley, et al. (2010) can be obtained from the characterization of the beta process as a Poisson process. Specifically, we show that the mean measure of the underlying Poisson process is equal to that of the beta process. We use this underlying re…
The fractional Poisson process (FPP) is a counting process with independent and identically distributed inter-event times following the Mittag-Leffler distribution. This process is very useful in several fields of applied and theoretical physics including models for anomalous diffusion. Contrary to the well-known Poiss…
A deep Neyman-Scott process uses Poisson processes for efficient inference in complex point processes.
A beta-negative binomial (BNB) process is proposed, leading to a beta-gamma-Poisson process, which may be viewed as a "multi-scoop" generalization of the beta-Bernoulli process. The BNB process is augmented into a beta-gamma-gamma-Poisson hierarchical structure, and applied as a nonparametric Bayesian prior for an infi…
Using the idea of a generalized Kaehler structure, which is a pair of commuting generalized complex structures, we construct bihermitian metrics on the projective plane and the product of two projective lines, and show that any such structure on a compact 4-manifold M defines one on the moduli space of anti-self-dual c…
Results on derivations and automorphisms of some quantum and classical Poisson algebras, as well as characterizations of manifolds by the Lie structure of such algebras, are revisited and extended. We prove in particular somehow unexpected fact that the algebras of linear differential operators acting on smooth section…
Study shows convergence rates for BSDEs approximated by compound Poisson processes.
New methods improve estimation of nonhomogeneous Poisson processes from limited data.
Proposes a model for predicting events from event streams.
Study shows Merton model limits to Poisson process with log-normal intensity, improving default portfolio prediction.
This paper analyzes optimal stopping regions for American options with Poisson exercise opportunities.
Paper improves fraud detection in imbalanced financial data.
Study of bandit problem with Poisson decision times and Lévy processes.
Efficiently infers Poisson process intensity using Gaussian process with sigmoid link.
Construct opers with apparent singularities from λ-connections on Riemann surfaces.
We introduce an algorithm for the segmentation of a class of regime switching processes. The segmentation algorithm is a non parametric statistical method able to identify the regimes (patches) of the time series. The process is composed of consecutive patches of variable length, each patch being described by a station…
We present a probabilistic model of events in continuous time in which each event triggers a Poisson process of successor events. The ensemble of observed events is thereby modeled as a superposition of Poisson processes. Efficient inference is feasible under this model with an EM algorithm. Moreover, the EM algorithm …
Establishes a microstructural foundation for a rough log-normal volatility model.
We present an approach to Jacobi and contact geometry that makes many facts, presented in the literature in an overcomplicated way, much more natural and clear. The key concepts are Kirillov manifolds and linear Kirillov structures, i.e., homogeneous Poisson manifolds and, respectively, homogeneous linear Poisson manif…
A new Bayesian optimization method using Poisson process for better noise robustness.
A bandit problem with filtered Poisson process data.
This thesis revises phase space concepts in physics, incorporating physical dimensions.
Study of lengths of cycles in large genus random maps converging to Poisson process.
Despite the fundamental nature of the inhomogeneous Poisson process in the theory and application of stochastic processes, and its attractive generalizations (e.g. Cox process), few tractable nonparametric modeling approaches of intensity functions exist, especially when observed points lie in a high-dimensional space.…
Study of line congruences for Appell's rank-4 hypergeometric functions.
A general construction of an sh Lie algebra from a homological resolution of a Lie algebra is given. It is applied to the space of local functionals equipped with a Poisson bracket, induced by a bracket for local functions along the lines suggested by Gel'fand, Dickey and Dorfman. In this way, higher order maps are con…
We study the geometric quantization process for twisted Poisson manifolds. First, we introduce the notion of Lichnerowicz-twisted Poisson cohomology for twisted Poisson manifolds and we use it in order to characterize their prequantization bundles and to establish their prequantization condition. Next, we introduce a p…
This paper solves mapping problems with a novel Gibbs sampling method.
The paper proposes a noncommutative deformation of toric varieties.
The seemingly disjoint problems of count and mixture modeling are united under the negative binomial (NB) process. A gamma process is employed to model the rate measure of a Poisson process, whose normalization provides a random probability measure for mixture modeling and whose marginalization leads to an NB process f…
Enhances count process modelling with Markov-modulated non-homogeneous Poisson process.
Study on critical faces convergence in a Poisson point process.
Efficient variational inference for Gaussian-process-modulated Poisson processes with panel count data.
In this note we study the optimal dividend problem for a company whose surplus process, in the absence of dividend payments, evolves as a generalized compound Poisson model in which the counting process is a generalized Poisson process. This model including the classical risk model and the Polya-Aeppli risk model as sp…