Related papers: Bivariate Tempered Space-Fractional Poisson Proces…

We explore the concept of a consistent exchangeable survival process - a joint distribution of survival times in which the risk set evolves as a continuous-time Markov process with homogeneous transition rates. We show a correspondence with…

This paper introduces a discrete-time fractional Poisson process defined as a renewal process, where the waiting times follow a discrete Mittag-Leffler distribution. We investigate its fundamental properties by explicitly deriving the…

In this paper, we show that the mixed fractional Poisson process (MFPP) exhibits the long-range dependence (LRD) property. It is proved by establishing an asymptotic result for the covariance of inverse mixed stable subordinator. Also, it…

Subordinators are infinitely divisible distributions on the positive half-line. They are often used as mixing distributions in Poisson mixtures. We show that appropriately scaled Poisson mixtures can approximate the mixing subordinator and…

We extend the random walk framework to include compounded steps, providing first-passage time (FPT) properties for a new class of superdiffusive processes, which are governed by the space-fractional spectral Fokker-Planck equation. This…

Hawkes process (HP) is a point process with a conditionally dependent intensity function. This paper defines the tempered fractional Hawkes process (TFHP) by time-changing the HP with an inverse tempered stable subordinator. We obtained…

Feature selection procedures for spatial point processes parametric intensity estimation have been recently developed since more and more applications involve a large number of covariates. In this paper, we investigate the setting where the…

We provide asymptotic results and develop high frequency statistical procedures for time-changed L\'evy processes sampled at random instants. The sampling times are given by first hitting times of symmetric barriers whose distance with…

Extreme environmental events frequently exhibit spatial and temporal dependence. These data are often modeled using max stable processes (MSPs). MSPs are computationally prohibitive to fit for as few as a dozen observations, with supposed…

In machine learning, it is commonly assumed that training and test data share the same population distribution. However, this assumption is often violated in practice because the sample selection bias may induce the distribution shift from…

The aim of this paper, is to define a bivariate exponentiated generalized linear exponential distribution based on Marshall-Olkin shock model. Statistical and reliability properties of this distribution are discussed. This includes…

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…

Different change-point type models encountered in statistical inference for stochastic processes give rise to different limiting likelihood ratio processes. In a previous paper of one of the authors it was established that one of these…

Time-changed stochastic processes have attracted great attention and wide interests due to their extensive applications, especially in financial time series, biology and physics. This paper pays attention to a special stochastic process,…

In this article, we study the potential theory of normal tempered stable process which is obtained by time-changing the Brownian motion with a tempered stable subordinator. Precisely, we study the asymptotic behavior of potential density…

In this paper, we study the Cauchy problem for backward stochastic partial differential equations (BSPDEs) involving fractional Laplacian operator. Firstly, by employing the martingale representation theorem and the fractional heat kernel,…

We use the two-time scale subordination in order to describe dynamical processes in continuous media with a long-term memory. Our consideration touches two physical examples in detail. First we study a temporal evolution of the species…

This paper focuses on hypothesis testing for the input of a L\'evy-driven storage system by sampling of the storage level. As the likelihood is not explicit we propose two tests that rely on transformation of the data. The first approach…

Fractional generalizations of the Poisson process and branching Furry process are considered. The link between characteristics of the processes, fractional differential equations and Levy stable densities are discussed and used for…

In this paper, time delay effect and distributed shear are considered in the Kuramoto model. On the Ott-Antonsen's manifold, through analyzing the associated characteristic equation of the reduced functional differential equation, the…