arXiv research

New method uses topological features for chatter detection in turning processes.

This paper aims to provide a simple modelling of speculative bubbles and derive some quantitative properties of its dynamical evolution. Starting from a description of individual speculative behaviours, we build and study a second order Markov process, which after simple transformations can be viewed as a turning two-d…

Develops Bilateral Gamma processes for financial market modeling.

We find the explicit expression for the equilibrium wealth distribution of the Directed Random Market process, recently introduced by Martínez-Martínez and López-Ruiz, which turns out to be a Gamma distribution with shape parameter $\frac{1}{2}$. We also prove the convergence of the discrete-time process describing the…

We extend the calculus of multiplicative vector fields and differential forms and their intrinsic derivatives from Lie groups to Lie groupoids; this generalization turns out to include also the classical process of complete lifting from arbitrary manifolds to tangent and cotangent bundles. Using this calculus we give a…

We derive the explicit formula for the joint Laplace transform of the Wishart process and its time integral which extends the original approach of Bru. We compare our methodology with the alternative results given by the variation of constants method, the linearization of the Matrix Riccati ODE's and the Runge-Kutta al…

Batch normalization with regularization turns deterministic autoencoders into generative models.

This report is concerned with the Mondrian process and its applications in machine learning. The Mondrian process is a guillotine-partition-valued stochastic process that possesses an elegant self-consistency property. The first part of the report uses simple concepts from applied probability to define the Mondrian pro…

Investigates existence of affine models for Lévy-driven term structures.

Authors prove the existence of a martingale measure in credit risk models.

Study on gamma-related OU processes with simulation methods.

Chatter identification and detection in machining processes has been an active area of research in the past two decades. Part of the challenge in studying chatter is that machining equations that describe its occurrence are often nonlinear delay differential equations. The majority of the available tools for chatter id…

Advanced 3D metrology technologies such as Coordinate Measuring Machine (CMM) and laser 3D scanners have facilitated the collection of massive point cloud data, beneficial for process monitoring, control and optimization. However, due to their high dimensionality and structure complexity, modeling and analysis of point…

We analyze a method to produce pairs of non independent Poisson processes $M(t),N(t)$ from positively correlated, self-decomposable, exponential renewals. In particular the present paper provides the family of copulas pairing the renewals, along with the closed form for the joint distribution $p_{m,n}(s,t)$ of the pair…

We study asymptotic properties of maximum likelihood estimators of drift parameters for a jump-type Heston model based on continuous time observations, where the jump process can be any purely non-Gaussian Lévy process of not necessarily bounded variation with a Lévy measure concentrated on $(-1,\infty)$. We prove stro…

Paper outlines a new mathematical language for experiments.

We propose a finite difference scheme to simulate solutions to a certain type of hyperbolic stochastic partial differential equation (HSPDE). These solutions can in turn estimate so called volatility modulated Volterra (VMV) processes and Lévy semistationary (LSS) processes, which is a class of processes that have been…

The beta-Bernoulli process provides a Bayesian nonparametric prior for models involving collections of binary-valued features. A draw from the beta process yields an infinite collection of probabilities in the unit interval, and a draw from the Bernoulli process turns these into binary-valued features. Recent work has …

We consider an insurance entity endowed with an initial capital and a surplus process modelled as a Brownian motion with drift. It is assumed that the company seeks to maximise the cumulated value of expected discounted dividends, which are declared or paid in a foreign currency. The currency fluctuation is modelled as…

Efficient algorithm for learning from indirect feedback in complex decision-making scenarios.

New algorithm solves uncertain Markov decision processes using Wasserstein uncertainty.

Gradient boosting can be seen as Gaussian process inference.

We examined the use of three conventional anomaly detection methods and assess their potential for on-line tool wear monitoring. Through efficient data processing and transformation of the algorithm proposed here, in a real-time environment, these methods were tested for fast evaluation of cutting tools on CNC machines…

GP-ALPS automatically selects latent processes for multi-output GPs.

We study the effect of investor inertia on stock price fluctuations with a market microstructure model comprising many small investors who are inactive most of the time. It turns out that semi-Markov processes are tailor made for modelling inert investors. With a suitable scaling, we show that when the price is driven …

The paper deals with the problem of identifying the internal dependencies and similarities among a large number of random processes. Linear models are considered to describe the relations among the time series and the energy associated to the corresponding modeling error is the criterion adopted to quantify their simil…

Foundation models struggle with multi-turn exploration but can learn through regular summaries.

We consider the problem of pricing derivatives written on some industrial loss index via utility indifference pricing. The industrial loss index is modelled by a compound Poisson process and the insurer can adjust her portfolio by choosing the risk loading, which in turn determines the demand. We compute the price of a…

Researchers use Gaussian processes to approximate Lagrange multipliers for Maximum-Entropy distributions.

In this paper we introduce a new coherent cumulative risk measure on $\mathcal{R}_L^p$, the space of càdlàg processes having Laplace transform. This new coherent risk measure turns out to be tractable enough within a class of models where the aggregate claims is driven by a spectrally positive Lévy process. Moreover, w…

Stochastic delay differential equations (SDDE's) have been used for financial modeling. In this article, we study a SDDE obtained by the equation of a CIR process, with an additional fixed delay term in drift; in particular, we prove that there exists a unique strong solution (positive and integrable) which we call fix…

The paper defines and explores vector bundles that can be turned and their properties.

New Hida-Matérn kernels enable flexible process priors and efficient GP inference.

Establishes a microstructural foundation for a rough log-normal volatility model.

We demonstrate by mathematical analysis and systematic computer simulations that redistribution can lead to sustainable growth in a society. The human capital dynamics of each agent is described by a stochastic multiplicative process which, in the long run, leads to the destruction of individual human capital and the e…

Develops quasi-likelihood analysis for marked point processes and applies it to Hawkes processes.

We undertake a study of markets from the perspective of a financial agent with limited access to information. The set of wealth processes available to the agent is structured with reasonable economic properties, instead of the usual practice of taking it to consist of stochastic integrals against a semimartingale integ…

The paper simplifies complex mechanical systems with external forces.

Scientific explanation often requires inferring maximally predictive features from a given data set. Unfortunately, the collection of minimal maximally predictive features for most stochastic processes is uncountably infinite. In such cases, one compromises and instead seeks nearly maximally predictive features. Here, …

In this paper we propose a new model for volatility fluctuations in financial time series. This model relies on a non-stationary gaussian process that exhibits aging behavior. It turns out that its properties, over any finite time interval, are very close to continuous cascade models. These latter models are indeed wel…

These lectures notes aim at introducing Lévy processes in an informal and intuitive way, accessible to non-specialists in the field. In the first part, we focus on the theory of Lévy processes. We analyze a `toy' example of a Lévy process, viz. a Lévy jump-diffusion, which yet offers significant insight into the distri…

Study shows subordinated Cramér-Lundberg model increases ruin probability.

Introduces tunable basis functions for Gaussian processes.

Agrachev's problem on circle turns is solved for various topologies.

In this paper, we identify the Bott connection on the natural foliation of the projective sphere bundle of a Finsler manifold to the Chern connection of this manifold. As a consequence, the symmetrization of the Bott connection turns out to be the Cartan connection of the Finsler manifold. Following Liu-Zhang \cite{Liu…

Deep networks can be approximated as Gaussian processes, linking training methods and kernel learning.

Enhances math problem-solving models with multi-turn preference learning.

Bayesian machine learning methods improve nowcasting with mixed frequency data.