Related papers: Fractional Generalizations of the Compound Poisson…
The aim of this paper is the analysis of the fractional Poisson process where the state probabilities $p_k^{\nu_k}(t)$, $t\ge 0$, are governed by time-fractional equations of order $0<\nu_k\leq 1$ depending on the number $k$ of events…
We analyze some basic issues associated with Generalized Poisson-Kac (GPK) stochastic processes, starting from the extended notion of the Markovian condition. The extended Markovian nature of GPK processes is established, and the…
This paper is devoted to the study of generalised time-fractional evolution equations involving Caputo type derivatives. Using analytical methods and probabilistic arguments we obtain well-posedness results and stochastic representations…
We introduce a new interpretation of sparse variational approximations for Gaussian processes using inducing points, which can lead to more scalable algorithms than previous methods. It is based on decomposing a Gaussian process as a sum of…
The generalized fractional Brownian motion is a Gaussian self-similar process whose increments are not necessarily stationary. It appears in applications as the scaling limit of a shot noise process with a power law shape function and…
We construct a compound Poisson process conditioned on its random summation that represents the sizes of the connected components in the sparse Erd\H{o}s-R\'enyi random graph $G(n,c/n)$. This new representation depicts a connection between…
This paper discusses properties of a Doubly Stochastic Poisson Process (DSPP) where the intensity process belongs to a class of affine diffusions. For any intensity process from this class we derive an analytical expression for probability…
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…
We derive an analytical expression of the inter-arrival time distribution for a non-homogeneous Poisson process (NHPP). This expression is exact and is applicable to any time interval, finite or infinite. As an illustration, we present…
Gaussian processes (GPs) are pervasive in functional data analysis, machine learning, and spatial statistics for modeling complex dependencies. Modern scientific data sets are typically heterogeneous and often contain multiple known…
We give a brief overview on the theory and phenomenology of generalized parton distributions (GPDs), including the recently developed framework of single-diffractive hard exclusive process for matching GPDs to experimental observables. We…
The mixed formulation of the classical Poisson problem introduces the flux as an additional variable, leading to a system of coupled equations. Using fractional calculus identities, in this work we explore a mixed formulation of the…
Gaussian process (GP) methods have been widely studied recently, especially for large-scale systems with big data and even more extreme cases when data is sparse. Key advantages of these methods consist in: 1) the ability to provide…
Learning control policies for real-world robotic tasks often involve challenges such as multimodality, local discontinuities, and the need for computational efficiency. These challenges arise from the complexity of robotic environments,…
A simple explicit construction is provided of a partition-valued fragmentation process whose distribution on partitions of $[n]=\{1,...,n\}$ at time $\theta \ge 0$ is governed by the Ewens sampling formula with parameter $\theta$. These…
In this paper we consider the relation between random sums and compositions of different processes. In particular, for independent Poisson processes $N_\alpha(t)$, $N_\beta(t)$, $t>0$, we show that $N_\alpha(N_\beta(t))…
We study a general non-homogeneous Skellam-type process with jumps of arbitrary fixed size. We express this process in terms of a linear combination of Poisson processes and study several properties, including the summation of independent…
The theory of sparse stochastic processes offers a broad class of statistical models to study signals. In this framework, signals are represented as realizations of random processes that are solution of linear stochastic differential…
Physical and mathematical applications of fractional Poisson probability distribution have been presented. As a physical application, a new family of quantum coherent states has been introduced and studied. As mathematical applications, we…
As a powerful tool for longitudinal data analysis, the generalized estimating equations have been widely studied in the academic community. However, in large-scale settings, this approach faces pronounced computational and storage…