Related papers: Interacting point processes
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…
The aim of this paper is to study some continuous-time bivariate Markov processes arising from group representation theory. The first component (level) can be either discrete (quasi-birth-and-death processes) or continuous (switching…
We present a class of stochastic processes in which the large deviation functions of time-integrated observables exhibit singularities that relate to dynamical phase transitions of trajectories. These illustrative examples include Brownian…
Stochastic models of sequential mutation acquisition are widely used to quantify cancer and bacterial evolution. Across manifold scenarios, recurrent research questions are: how many cells are there with $n$ alterations, and how long will…
We study supercritical branching processes under the influence of an i.i.d. emigration component. We provide conditions, under which the lifetime of the process is finite respectively has a finite expectation. A new version of the…
Point processes often have a natural interpretation with respect to a continuous process. We propose a point process construction that describes arrival time observations in terms of the state of a latent diffusion process. In this…
In this paper we will take under consideration subordinators and their inverse processes (hitting-times). We will present in general the governing equations of such processes by means of convolution-type integro-differential operators…
Point process models have been used to analyze interaction event times on a social network, in the hope to provides valuable insights for social science research. However, the diagnostics and visualization of the modeling results from such…
In a simplified model of Multiple Parton Interactions the inclusive cross sections, of processes with large momentum transfer exchange, acquire the statistical meaning of factorial moments of the distribution in multiplicity of…
We consider a Piecewise Deterministic Markov Process given by random switching between finitely many vector fields vanishing at $0$. It has been shown recently that the behaviour of this process is mainly determined by the signs of Lyapunov…
A study of time homogeneous, real valued Markov processes with a special property and a non-atomic initial distribution is provided. The new notion of a function of evolution of distribution which determines the dependency between one…
Representations of branching Markov processes and their measure-valued limits in terms of countable systems of particles are constructed for models with spatially varying birth and death rates. Each particle has a location and a "level,"…
Increased day-trading activity and the subsequent jump in intraday volatility and trading volume fluctuations has raised considerable interest in models for financial market microstructure. We investigate the random transitions between two…
Point processes in time have a wide range of applications that include the claims arrival process in insurance or the analysis of queues in operations research. Due to advances in technology, such samples of point processes are increasingly…
In this work we consider time series with a finite number of discrete point changes. We assume that the data in each segment follows a different probability density functions (pdf). We focus on the case where the data in all segments are…
Point processes model the distribution of random point sets in mathematical spaces, such as spatial and temporal domains, with applications in fields like seismology, neuroscience, and economics. Existing statistical and machine learning…
We consider the genealogical tree of a stationary continuous state branching process with immigration. For a sub-critical stable branching mechanism, we consider the genealogical tree of the extant population at some fixed time and prove…
In this paper, we propose a new comparison tool for spatial homogeneity of point processes, based on the joint examination of void probabilities and factorial moment measures. We prove that determinantal and permanental processes, as well…
Within the applications of spatial point processes, it is increasingly becoming common that events are labeled by marks, prompting an exploration beyond the spatial distribution of events by incorporating the marks in the undertaken…
We study general aspects of active motion with fluctuations in the speed and the direction of motion in two dimensions. We consider the case in which fluctuations in the speed are not correlated to fluctuations in the direction of motion,…