相关论文: Asymptotic absorption-time distributions in extinc…

In this paper we study an asymptotic expansion for the distribution of a random motion of a particle driven by a Markov process in diffusion approximation. We show that the singularly perturbed equation of a Markovian random motion can be…

We investigate some asymptotic properties of general Markov processes conditioned not to be absorbed by moving boundaries. We first give general criteria involving an exponential convergence towards the Q-process, that is the law of the…

The Moran process models the spread of mutations in populations on graphs. We investigate the absorption time of the process, which is the time taken for a mutation introduced at a randomly chosen vertex to either spread to the whole…

Scaling limits for continuous-time branching processes with discrete state space are provided as the initial state tends to infinity. Depending on the finiteness or non-finiteness of the mean and/or the variance of the offspring…

Systems that evolve towards a state from which they cannot depart are common in nature. But the fluctuation-dissipation theorem, a fundamental result in statistical mechanics, is mainly restricted to systems near-stationarity. In processes…

For a class of Gaussian stationary processes, we prove a limit theorem on the convergence of the distributions of the scaled last exit time over a slowly growing linear boundary. The limit is a double exponential (Gumbel) distribution.

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…

In this paper we study the long term evolution of a continuous time Markov chain formed by two interacting birth-and-death processes. The interaction between the processes is modelled by transition rates which are functions with suitable…

This study explores a Gaussian quasi-likelihood approach for estimating parameters of diffusion processes with Markovian regime switching. Assuming the ergodicity under high-frequency sampling, we will show the asymptotic normality of the…

In this paper, we discuss long-time behavior of sample paths for a wide range of regime-switching diffusions. Firstly, almost sure asymptotic stability is concerned (i) for regime-switching diffusions with finite state spaces by the…

We study that the breakdown of epidemic depends on some parameters, that is expressed in epidemic reproduction ratio number. It is noted that when $R_0 $ exceeds 1, the stochastic model have two different results. But, eventually the…

Consider a system evolving according to an absorbing discrete-time Markov chain with known transition matrix. The state of the system is observed at two points in time, separated by an unknown number of generations. We are interested in…

The expansion of global production networks has raised many important questions about the interdependence among countries and how future changes in the world economy are likely to affect the countries' positioning in global value chains. We…

We consider general Markov processes with absorption and provide criteria ensuring the exponential convergence in total variation of the distribution of the process conditioned not to be absorbed. The first one is based on two-sided…

This paper demonstrates a lower and upper solution method to investigate the asymptotic behaviour of the conservative reaction-diffusion systems associated with Markovian process algebra models. In particular, we have proved the uniform…

Studies of transient dynamics captures the time history of any dramatic changes in the dynamics of a system. The transient dynamics is investigated here in a classic ecological model of a bistable tri-trophic food chain. All the species in…

This paper is devoted to the analysis of the finite-dimensional distributions and asymptotic behavior of extremal Markov processes connected to the Kendall convolution. In particular, based on its stochastic representation, we provide…

We study the two-species diffusion-annihilation process, $A+B\rightarrow$ \O, on the fully-connected lattice. Probability distributions for the number of particles and the reaction time are obtained for a finite-size system using a master…

In this work we study the asymptotic of renewal sequences associated with certain transient renewal Markov chains and enquire about the existence of limit laws in this set up.

Many real epidemics of an infectious disease are not straightforwardly super- or sub-critical, and the understanding of epidemic models that exhibit such complexity has been identified as a priority for theoretical work. We provide insights…