相关论文: Multiplicity free actions, birth and death process…

Many examples of exactly solvable birth and death processes, a typical stationary Markov chain, are presented together with the explicit expressions of the transition probabilities. They are derived by similarity transforming exactly…

A coinless quantisation procedure of continuous and discrete time Birth and Death (BD) processes is presented. The quantum Hamiltonian H is derived by similarity transforming the matrix L describing the BD equation in terms of the square…

Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but they are structurally unable to describe stochastic fluctuations or population-size-dependent birth and death rates.…

We consider consistent dynamics for non-intersecting birth and death chains, originating from dualities of stochastic coalescing flows and one dimensional orthogonal polynomials. As corollaries, we obtain unified and simple probabilistic…

Based on the framework of Plamen Iliev, multivariate Meixner polynomials are constructed explicitly as Birth and Death polynomials. They form the complete set of eigenpolynomials of a birth and death process with the birth and death rates…

Given a birth-death process on $\mathbb {N}$ with semigroup $(P_t)_{t\geq0}$ and a discrete gradient ${\partial}_u$ depending on a positive weight $u$, we establish intertwining relations of the form ${\partial}_uP_t=Q_t\,{\partial}_u$,…

We study a class of quantum Markov processes that, on the one hand, is inspired by the micromaser experiment in quantum optics and, on the other hand, by classical birth and death processes. We prove some general geometric properties and…

In this paper, we consider multi-dimensional birth and death chains and continuous time quantum walks (CTQW) related to them. For CTQW related to our forms of multi-dimensional birth and death chains, we obtain the time scaled independence…

Markovian intertwining relations between two Markov semigroups are related to the partial inclusion of the spectra of their generators, at least for finite ergodic processes. We check the limitations of this observation by investigating the…

Spatial birth-and-death processes with a finite number of particles are obtained as unique solutions to certain stochastic equations. Conditions are given for existence and uniqueness of such solutions, as well as for continuous dependence…

We study the so-called multi-mixed fractional Brownian motions (mmfBm) and multi-mixed fractional Ornstein--Ulhenbeck (mmfOU) processes. These processes are constructed by mixing by superimposing (infinitely many) independent fractional…

In this article, we provide different representations for a time-fractional birth and death process $N_{\alpha}(t)$, whose transition probabilities are governed by a time-fractional system of differential equations. More specifically, we…

The Ornstein-Uhlenbeck process can be seen as a paradigm of a finite-variance and statistically stationary rough random walk. Furthermore, it is defined as the unique solution of a Markovian stochastic dynamics and shares the same local…

This paper investigates stochastic finite matrices and the corresponding finite Markov chains constructed using recurrence matrices for general families of orthogonal polynomials and multiple orthogonal polynomials. The paper explores the…

Growth-fragmentation processes describe systems of particles in which each particle may grow larger or smaller, and divide into smaller ones as time proceeds. Unlike previous studies, which have focused mainly on the self-similar case, we…

For a family of unital free *-algebras with a family of states on them, we construct a sequence of noncommutative probability spaces, which are tensor product algebras with tensor product states and which approximate the free product of…

The spatial symmetry property of truncated birth-death processes studied in Di Crescenzo [6] is extended to a wider family of continuous-time Markov chains. We show that it yields simple expressions for first-passage-time densities and…

We present a class of Gauss-Markov processes which can be represented as space-time scaled stationary Ornstein-Uhlenbeck processes defined on the real line. We give several explicit examples of the representation for certain Gauss bridge…

We introduce a family of Markov processes on set partitions with a bounded number of blocks, called Lipschitz partition processes. We construct these processes explicitly by a Poisson point process on the space of Lipschitz continuous maps…

This paper introduces several new classes of mathematical structures that have close connections with physics and with the theory of dynamical systems. The most general of these structures, called indivisible stochastic processes,…