Related papers: A Markovian Perspective on the Classical Occupancy…
Dispersion is a fundamental concept in statistics, yet standard approaches - especially via stochastic orders - face limitations in the discrete setting. In particular, the classical dispersive order, well-established for continuous…
For Markov processes with absorption, we provide general criteria ensuring the existence and the exponential non-uniform convergence in total variation norm to a quasi-stationary distribution. We also characterize a subset of its domain of…
The main topic of these notes are Markov loops, studied in the context of continuous time Markov chains on discrete state spaces. We refer to [1] and [2] for the short "history" of the subject. In contrast with these references, symmetry is…
In this paper, we study the existence and uniqueness of solutions for general fractional-time parabolic equations of mixture type, and their probabilistic representations in terms of the corresponding inverse subordinators with or without…
We study the Classical Probability analogue of the dilations of a quantum dynamical semigroup in Quantum Probability. Given a (not necessarily homogeneous) Markov chain in discrete time in a finite state space E, we introduce a second…
We consider the evolution of populations under the joint action of mutation and differential reproduction, or selection. The population is modelled as a finite-type Markov branching process in continuous time, and the associated…
We consider a discrete-time Markov chain, called fragmentation process, that describes a specific way of successively removing objects from a linear arrangement. The process arises in population genetics and describes the ancestry of the…
From the perspective of probability, the stability of growing network is studied in the present paper. Using the DMS model as an example, we establish a relation between the growing network and Markov process. Based on the concept and…
We study a generalized P\'{o}lya urn model with two types of ball. If the drawn ball is red, it is replaced together with a black ball, but if the drawn ball is black it is replaced and a red ball is thrown out of the urn. When only black…
We consider Palm distributions arising in a Markov process with time homogeneous transitions which is jointly stationary with multiple point processes. Motivated by a BAR approach studied in the recent paper Braverman, Dai and Miyazawa…
We consider an elementary model for self-organised criticality, the activated random walk on the complete graph. We introduce a discrete time Markov chain as follows. At each time step, we add an active particle at a random vertex and let…
We consider the time evolution of the supercritical Galton-Watson model of branching particles with extra parameter (mass). In the moment of the division the mass of the particle (which is growing linearly after the birth) is divided in…
We develop a recently introduced representation of quantum dynamics based on sampling negative Markov chain processes. By introducing particles and antiparticles, this formalism maps generic quantum dynamics onto a Markov process defined…
The Scrooge distribution is a probability distribution over the set of pure states of a quantum system. Specifically, it is the distribution that, upon measurement, gives up the least information about the identity of the pure state,…
The paper discusses a family of Markov processes that represent many particle systems, and their limiting behaviour when the number of particles go to infinity. The first part concerns model of biological systems: a model for sympatric…
In this note we connect the notion of solutions of a martingale problem to the notion of a strongly continuous and locally equi-continuous semigroup on the space of bounded continuous functions equipped with the strict topology. This…
In this paper, we consider the gradual-impulse control problem of continuous-time Markov decision processes, where the system performance is measured by the expectation of the exponential utility of the total cost. We prove, under very…
Perfect sampling is a technique that uses coupling arguments to provide a sample from the stationary distribution of a Markov chain in a finite time without ever computing the distribution. This technique is very efficient if all the events…
This paper generalizes the notion of stochastic order to a relation between probability measures over arbitrary measurable spaces. This generalization is motivated by the observation that for the stochastic ordering of two stationary Markov…
We introduce a novel reformulation of the mean-field system for pulse-coupled oscillators. It is based on writing a closed equation for the inverse distribution function associated to the probability density of oscillators with a given…