Related papers: Generalized Fractional Counting Process

The paper introduces the concept of a cluster structure to define a joint distribution of the sample size and its exchangeable random partitions. The cluster structure allows the probability distribution of the random partitions of a subset…

Deploying trustworthy AI systems requires principled uncertainty quantification. Conformal prediction (CP) is a widely used framework for constructing prediction sets with distribution-free coverage guarantees. In many practical settings,…

Neural models for amortized probabilistic clustering yield samples of cluster labels given a set-structured input, while avoiding lengthy Markov chain runs and the need for explicit data likelihoods. Existing methods which label each data…

We consider the general branching random walk under minimal assumptions, which in particular guarantee that the empirical particle distribution admits an almost sure central limit theorem. For such a process, we study the large time decay…

In this paper, we study a generalized version of the Poisson-type process by time-changing it with the geometric counting process. Our work generalizes the work done by Meoli (2023) \cite{meoli2023some}. We defined the geometric…

We study the process of suitably normalized successive return times to rare events in the setting of infinite-measure preserving dynamical systems. Specifically, we consider small neighborhoods of points whose measure tends to zero. We…

In this article, a high-order time-stepping scheme based on the cubic interpolation formula is considered to approximate the generalized Caputo fractional derivative (GCFD). Convergence order for this scheme is $(4-\alpha)$, where $\alpha…

Tree structures are ubiquitous in data across many domains, and many datasets are naturally modelled by unobserved tree structures. In this paper, first we review the theory of random fragmentation processes [Bertoin, 2006], and a number of…

In this article, we quantify the functional convergence of the rescaled random walk with heavy tails to a stable process.This generalizes the Generalized Central Limit Theorem for stable random variables infinite dimension. We show that…

We consider the problem of inference for the states and parameters of a continuous-time multitype branching process from partially observed time series data. Exact inference for this class of models, typically using sequential Monte Carlo,…

A representation of Gaussian distributed sparsely sampled longitudinal data in terms of predictive distributions for their functional principal component scores (FPCs) maps available data for each subject to a multivariate Gaussian…

To extend several known centered Gaussian processes, we introduce a new centered mixed self-similar Gaussian process called the mixed generalized fractional Brownian motion, which could serve as a good model for a larger class of natural…

The combination of inducing point methods with stochastic variational inference has enabled approximate Gaussian Process (GP) inference on large datasets. Unfortunately, the resulting predictive distributions often exhibit substantially…

The partial differential equation of Gaussian diffusion is generalized by using the time-fractional derivative of distributed order between 0 and 1, in both the Riemann-Liouville (R-L) and the Caputo (C) sense. For a general distribution of…

We provide a generalization of Theorem 1 in Bartkiewicz, Jakubowski, Mikosch and Wintenberger (2011) in the sense that we give sufficient conditions for weak convergence of finite dimensional distributions of the partial sum processes of a…

Geostatistics is a branch of statistics concerned with stochastic processes over continuous domains, with Gaussian processes (GPs) providing a flexible and principled modelling framework. However, the high computational cost of simulating…

We introduce a scalable approach to Gaussian process inference that combines spatio-temporal filtering with natural gradient variational inference, resulting in a non-conjugate GP method for multivariate data that scales linearly with…

The Poisson process is one of the simplest stochastic processes defined in continuous time, having interesting mathematical properties, leading, in many situations, to applications mathematically treatable. One of the limitations of the…

We analyze a class of continuous time random walks in $\mathbb R^d,d\geq 2,$ with uniformly distributed directions. The steps performed by these processes are distributed according to a generalized Dirichlet law. Given the number of changes…

A physical-mathematical approach to anomalous diffusion may be based on fractional diffusion equations and related random walk models. The fundamental solutions of these equations can be interpreted as probability densities evolving in time…