Related papers: On Time-Changed Birth-Death Processes with Catastr…
We investigate the first-passage properties of a jump process with a constant drift, focusing on two key observables: the first-passage time $\tau$ and the number of jumps $n$ before the first-passage event. By mapping the problem onto an…
We study general stochastic birth and death processes including delay. We develop several approaches for the analytical treatment of these non-Markovian systems, valid, not only for constant delays, but also for stochastic delays with…
We develop a likelihood-based inference for finite-state birth-death processes with composite birth rates, in which multiple distinct mechanisms contribute additively to the total birth intensity. Our main motivating example is an SIS…
The first chapter concerns monotype population models. We first study general birth and death processes and we give non-explosion and extinction criteria, moment computations and a pathwise representation. We then show how different scales…
The first-passage time is proposed as an independent thermodynamic parameter of the statistical distribution that generalizes the Gibbs distribution. The theory does not include the determination of the first passage statistics itself. A…
We consider a run-and-tumble particle on a half-line with an absorbing target at the origin. The particle has an internal velocity state that switches between two opposite values at Poisson-distributed times. The position of the particle…
We recently proposed a method for estimation of states and parameters in stochastic differential equations, which included intermediate time points between observations and used the Laplace approximation to integrate out these intermediate…
In this paper, we study a birth and death process $\{N_t\}_{t\ge0}$ on positive half lattice, which at each discontinuity jumps at most a distance $R\ge 1$ to the right or exactly a distance $1$ to the left. The transitional probabilities…
Random population dynamics with catastrophes (events pertaining to possible elimination of a large portion of the population) has a long history in the mathematical literature. In this paper we study an ergodic model for random population…
In this paper we explore the life expectancy limits by based on the stochastic modeling of mortality and applying the first exit or hitting time theory of a stochastic process. The main assumption is that the health state or the "vitality",…
We examine birth--death processes with state dependent transition probabilities and at least one absorbing boundary. In evolution, this describes selection acting on two different types in a finite population where reproductive events occur…
The paper gives a systematic analysis of singularities of transition processes in dynamical systems. General dynamical systems with dependence on parameter are studied. A system of relaxation times is constructed. Each relaxation time…
Catastrophes of all kinds can be roughly defined as short duration-large amplitude events following and followed by long periods of "ripening". Major earthquakes surely belong to the class of 'catastrophic' events. Because of the space-time…
We analyze a modification of the Richards growth model by introducing a time-dependent perturbation in the growth rate. This modification becomes effective at a special switching time, which represents the first-crossing-time of the…
In a recent paper in the Journal of Theoretical Probability Gong, Mao and Zhang, using the theory of Dirichlet forms, extended Karlin and McGregor's classical results on first-hitting times of a birth-death process on the nonnegative…
In this paper we introduce the concept of random time changes in dynamical systems. The subordination principle may be applied to study the long time behavior of the random time systems. We show, under certain assumptions on the class of…
This paper is not (or at least not only) about human infant mortality. In line with reliability theory, "infant" will refer here to the time interval following birth during which the mortality (or failure) rate decreases. This definition…
A method yielding simple relationships among bilateral birth-and-death processes is outlined. This allows one to relate birth and death rates of two processes in such a way that their transition probabilities, first-passage-time densities…
Many researchers have investigated first hitting times as models for survival data. First hitting times arise naturally in many types of stochastic processes, ranging from Wiener processes to Markov chains. In a survival context, the state…
This paper is focused on a class of spatial birth and death process of the Euclidean space where the birth rate is constant and the death rate of a given point is the shot noise created at its location by the other points of the current…