Related papers: Student t-L\'evy regression model in YUIMA
This paper investigates L\'evy walks with random velocities, extending classical models beyond constant speed assumptions. We derive scaling limits, demonstrating that diffusion depends on interplay between heavy-tailed duration and…
If a document is about travel, we may expect that short snippets of the document should also be about travel. We introduce a general framework for incorporating these types of invariances into a discriminative classifier. The framework…
The score function for the diffusion process, also known as the gradient of the log-density, is a basic concept to characterize the probability flow with important applications in the score-based diffusion generative modelling and the…
In this paper we study the effective degrees of freedom of a general class of reduced rank estimators for multivariate regression in the framework of Stein's unbiased risk estimation (SURE). We derive a finite-sample exact unbiased…
The dream of achieving a student-teacher ratio of 1:1 is closer than ever thanks to the emergence of large language models (LLMs). One potential application of these models in the educational field would be to provide feedback to students…
Motivated by the construction of the It\^o stochastic integral, we consider a step function method to discretize and simulate volatility modulated L\'evy semistationary processes. Moreover, we assess the accuracy of the method with a…
We present a perturbation theory by extending a prescription due to Feynman for computing the probability density function for the random flight motion. The method can be applied to a wide variety of otherwise difficult circumstances. The…
One of the emergent challenges of student work submitted for assessment is the widespread use of large language models (LLMs) to support and even produce written work. This particularly affects subjects where long-form written work is a key…
We study the small-time asymptotics of sample paths of L\'evy processes and L\'evy-type processes. Namely, we investigate under which conditions the limit $$\limsup_{t \to 0} \frac{1}{f(t)} |X_t-X_0|$$ is finite resp.\ infinite with…
Educational interventions are effective tools for enhancing student learning. While Large Language Models (LLMs) allow for generating adaptive feedback at scale, current studies lack clear methodologies for providing Just-in-Time (JiT)…
An R package for specifying and estimating linear latent variable models is presented. The philosophy of the implementation is to separate the model specification from the actual data, which leads to a dynamic and easy way of modeling…
Existing data-free model stealing methods use a generator to produce samples in order to train a student model to match the target model outputs. To this end, the two main challenges are estimating gradients of the target model without…
Stable distributions are a celebrated class of probability laws used in various fields. The $\alpha$-stable process, and its exponentially tempered counterpart, the Classical Tempered Stable (CTS) process, are also prominent examples of…
Irregular Multivariate Time Series (IMTS) are characterized by uneven intervals between consecutive timestamps, which carry sampling pattern information valuable and informative for learning temporal and variable dependencies. In addition,…
Instruction-following made modern large language models (LLMs) helpful assistants. However, the key to taming LLMs on complex instructions remains mysterious, for that there are huge gaps between models trained by open-source community and…
We experimentally investigate the transmission of light by dense atomic vapor. The light propagating in dense atomic vapor can be modeled as a L\'evy flight random walk. For such system, the step-length distribution can be modeled as…
In this paper, we study the L\'evy process time-changed by independent L\'evy subordinators, namely, the incomplete gamma subordinator, the $\epsilon$-jumps incomplete gamma subordinator and tempered incomplete gamma subordinator. We derive…
This article treats long term average impulse control problems with running costs in the case that the underlying process is a L\'evy process. Under quite general conditions we characterize the value of the control problem as the value of a…
Continuous-time autoregressive and moving average (CARMA) models are extensively used to model high-frequency and irregularly sampled data. We study Whittle estimation for the model parameters when the process is observed at renewal times.…
We develop the information geometry of L\'evy processes. Deriving $\alpha$-divergences directly in terms of the L\'evy triplets of the L\'evy processes, we identify Fisher information matrix and $\alpha$-connection on the statistical…