相关论文: A generating function approach to Markov chains un…
We establish general theorems quantifying the notion of recurrence --- through an estimation of the moments of passage times --- for irreducible continuous-time Markov chains on countably infinite state spaces. Sharp conditions of…
Stochastic reaction networks are mathematical models with a wide range of applications in biochemistry, ecology, and epidemiology, and are often complex to analyze. Except for some special cases, it is generally difficult to predict how the…
A Markovian model of group-structured (two-level) population dynamics features births, deaths, and migrations of individuals, and fission and extinction of groups. These models are useful for studying group selection and other evolutionary…
Evolutionary game theory has traditionally employed deterministic models to describe population dynamics. These models, due to their inherent nonlinearities, can exhibit deterministic chaos, where population fluctuations follow complex,…
This work demonstrates the application of a birth-death Markov process, inspired by radioactive decay, to capture the dynamics of innovation processes. Leveraging the Bass diffusion model, we derive a Gompertz-like function explaining the…
Intervals between discrete events representing human activities, as well as other types of events, often obey heavy-tailed distributions, and their impacts on collective dynamics on networks such as contagion processes have been intensively…
The recent interest in human dynamics has led researchers to investigate the stochastic processes that explain human behaviour in different contexts. Here we propose a generative model to capture the essential dynamics of survival analysis,…
Genetic data are often used to infer demographic history and changes or detect genes under selection. Inferential methods are commonly based on models making various strong assumptions: demography and population structures are supposed…
In evolutionary processes, population structure has a substantial effect on natural selection. Here, we analyze how motion of individuals affects constant selection in structured populations. Motion is relevant because it leads to changes…
The birth-death process is a special type of continuous-time Markov chain with index set $\mathbb{N}$. Its resolvent matrix can be fully characterized by a set of parameters $(\gamma, \beta, \nu)$, where $\gamma$ and $\beta$ are…
In this work we address the analysis of discrete-time models of structured metapopulations subject to environmental stochasticity. Previous works on these models made use of the fact that migrations between the patches can be considered…
We characterize recurrence and transience of nonnegative multivariate autoregressive processes of order one with random contractive coefficient matrix, of subcritical multitype Galton-Watson branching processes in random environment with…
The theory of ``Markov-up'' processes is being developed. This is a new class of stochastic processes with ``partial'' markovian features; it could also be called ``one-sided Markov''. Such a behavior may be found in the real world and in…
General birth-and-death as well as hopping stochastic dynamics of infinite particle systems in the continuum are considered. We derive corresponding evolution equations for correlation functions and generating functionals. General…
We formulate some simple conditions under which a Markov chain may be approximated by the solution to a differential equation, with quantifiable error probabilities. The role of a choice of coordinate functions for the Markov chain is…
It is shown that the combinatorics of commutation relations is well suited for analyzing the convergence rate of certain Markov chains. Examples studied include random walk on irreducible representations, a local random walk on partitions…
The paper considers a particular family of set--valued stochastic processes modeling birth--and--growth processes. The proposed setting allows us to investigate the nucleation and the growth processes. A decomposition theorem is established…
This paper considers the cycle maximum in birth-death processes as a stepping stone to characterisation of the cycle maximum in single queues and open Kelly-Whittle networks of queues. For positive recurrent birth-death processes we show…
We show that evolutionary computation can be implemented as standard Markov-chain Monte-Carlo (MCMC) sampling. With some care, `genetic algorithms' can be constructed that are reversible Markov chains that satisfy detailed balance; it…
Understanding the statistical properties of a collection of individuals subject to random displacements and birth-and-death events is key to several applications in physics and life sciences, encompassing the diagnostic of nuclear reactors…