Related papers: Student t-L\'evy regression model in YUIMA
The rapid integration of Large Language Models (LLMs) into software engineering practice is reshaping how software testing activities are performed. LLMs are increasingly used to support software testing. Consequently, software testing…
We present a class of L\'evy processes for modelling financial market fluctuations: Bilateral Gamma processes. Our starting point is to explore the properties of bilateral Gamma distributions, and then we turn to their associated L\'evy…
We propose a new testing procedure about the tail weight parameter of multivariate Student $t$ distributions by having recourse to the Le Cam methodology. Our test is asymptotically as efficient as the classical likelihood ratio test, but…
An obvious way to simulate a L\'evy process $X$ is to sample its increments over time $1/n$, thus constructing an approximating random walk $X^{(n)}$. This paper considers the error of such approximation after the two-sided reflection map…
Consider the following stochastic differential equation (SDE) $$dX_t = b(t,X_{t-}) \, dt+ dL_t, \quad X_0 = x,$$ driven by a $d$-dimensional L\'evy process $(L_t)_{t \geq 0}$. We establish conditions on the L\'evy process and the drift…
In this paper we investigate two numerical schemes for the simulation of stochastic Volterra equations driven by space--time L\'evy noise of pure-jump type. The first one is based on truncating the small jumps of the noise, while the second…
We provide a new non-parametric Fourier procedure to estimate the trajectory of the instantaneous covariance process (from discrete observations of a multidimensional price process) in the presence of jumps extending the seminal work…
In many longitudinal settings, economic theory does not guide practitioners on the type of restrictions that must be imposed to solve the rotational indeterminacy of factor-augmented linear models. We study this problem and offer several…
Traditional Large Language Model (LLM) pretraining relies on autoregressive language modeling with randomly sampled data from web-scale datasets. Inspired by human learning techniques like spaced repetition, we hypothesize that random…
The aim of this paper is to develop estimation and inference methods for the drift parameters of multivariate L\'evy-driven continuous-time autoregressive processes of order $p\in\mathbb{N}$. Starting from a continuous-time observation of…
We construct intrinsic on-and off-diagonal upper and lower estimates for the transition probability density of a L\'evy process in small time. By intrinsic we mean that such estimates reflect the structure of the characteristic exponent of…
The crossover among two or more types of diffusive processes represents a vibrant theme in nonequilibrium statistical physics. In this work we propose two models to generate crossovers among different L\'evy processes: in the first model we…
This paper introduces a fully Bayesian analysis of mixture autoregressive models with Student t components. With the capacity of capturing the behaviour in the tails of the distribution, the Student t MAR model provides a more flexible…
It is a critical challenge to efficiently unlock the powerful reasoning potential of Large Language Models (LLMs) for specific tasks or new distributions. Existing test-time adaptation methods often require tuning model parameters, which is…
L\'evy processes are widely used in financial mathematics to model return data. Price processes are then defined as a corresponding geometric L\'evy process, implying the fact that returns are independent. In this paper we propose an…
Gaussian process priors are commonly used in aerospace design for performing Bayesian optimization. Nonetheless, Gaussian processes suffer two significant drawbacks: outliers are a priori assumed unlikely, and the posterior variance…
In the face of the upcoming 30th anniversary of econophysics, we review our contributions and other related works on the modeling of the long-range memory phenomenon in physical, economic, and other social complex systems. Our group has…
We analyze the Levy processes produced by means of two interconnected classes of non stable, infinitely divisible distribution: the Variance Gamma and the Student laws. While the Variance Gamma family is closed under convolution, the…
We consider a queuing model with the workload evolving between consecutive i.i.d.\ exponential timers $\{e_q^{(i)}\}_{i=1,2,...}$ according to a spectrally positive L\'evy process $Y_i(t)$ that is reflected at zero, and where the…
Joint models for longitudinal and survival data have gained a lot of attention in recent years, with the development of myriad extensions to the basic model, including those which allow for multivariate longitudinal data, competing risks…