相关论文: Generalized Space Time Fractional Skellam Process

The aim of this paper is to investigate how the correlation properties of a stationary Markovian stochastic processes affect the First Passage Time distribution. First Passage Time issues are a classical topic in stochastic processes…

Gaussian processes are probabilistic models that are commonly used as functional priors in machine learning. Due to their probabilistic nature, they can be used to capture the prior information on the statistics of noise, smoothness of the…

Gaussian processes are the leading class of distributions on random functions, but they suffer from well known issues including difficulty scaling and inflexibility with respect to certain shape constraints (such as nonnegativity). Here we…

Gaussian-process state-space models (GP-SSMs) provide a flexible nonparametric alternative for modeling time-series dynamics that are nonlinear or difficult to specify parametrically. While the Kalman filter is effective for linear-Gaussian…

This paper deals with uncertainty propagation of general stochastic hybrid systems (GSHS) where the continuous state space is a compact Lie group. A computational framework is proposed to solve the Fokker-Planck (FP) equation that describes…

This text is a survey of the general theory of stochastic processes, with a view towards random times and enlargements of filtrations. The first five chapters present standard materials, which were developed by the French probability school…

A Gaussian process (GP)-based methodology is proposed to emulate complex dynamical computer models (or simulators). The method relies on emulating the numerical flow map of the system over an initial (short) time step, where the flow map is…

This paper establishes the theoretical foundation for statistical applications of an intriguing new type of spatial point processes called critical point processes. These point processes, residing in Euclidean space, consist of the critical…

We study a class of stochastic processes of the type $\frac{d^n x}{dt^n}= v_0\, \sigma(t)$ where $n>0$ is a positive integer and $\sigma(t)=\pm 1$ represents an `active' telegraphic noise that flips from one state to the other with a…

This paper proposes a novel Generalized Non-Standard Finite Difference (GNSFD) scheme for the numerical solution of a class of fractional partial differential equations (FrPDEs). The formulation of the method is grounded in optimization and…

Discrete time spatial time series data arise routinely in meteorological and environmental studies. Inference and prediction associated with them are mostly carried out using any of the several variants of the linear state space model that…

In principle, the generalized master equation can be used to efficiently compute the macroscopic first passage time (FPT) distribution of a complex stochastic system from short-term microscopic simulation data. However, computing its…

In this paper we describe some properties of the generalized Gram-Schmidt procedure (GGSP) for generating Parseval frames which was first introduced by Casazza and Kutyniok [A generalization of Gram-Schmidt orthogonalization generating all…

Gaussian process regression is a powerful Bayesian nonlinear regression method. Recent research has enabled the capture of many types of observations using non-Gaussian likelihoods. To deal with various tasks in spatial modeling, we benefit…

The paper investigates the rich class of Generalized Tempered Stable distribution, an alternative to Normal distribution and the $\alpha$-Stable distribution for modelling asset return and many physical and economic systems. Firstly, we…

Sample Space Reducing (SSR) processes are simple stochastic processes that offer a new route to understand scaling in path-dependent processes. Here we define a cascading process that generalises the recently defined SSR processes and is…

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…

It is our intention to provide via fractional calculus a generalization of the pure and compound Poisson processes, which are known to play a fundamental role in renewal theory, without and with reward, respectively. We first recall the…

We construct admissible circulant Laplacian matrix functions as generators for strictly increasing random walks on the integer line. These Laplacian matrix functions refer to a certain class of Bernstein functions. The approach has…

Gaussian processes are flexible probabilistic regression models which are widely used in statistics and machine learning. However, a drawback is their limited scalability to large data sets. To alleviate this, full-scale approximations…