Related papers: Approximation for extinction probability of the co…
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…
We consider the problem of extinction processes on random networks with a given structure. For sufficiently large well-mixed populations, the process of extinction of one or more state variable components occurs in the tail of the…
This article studies the quasi-stationary behaviour of absorbed one-dimensional diffusion processes with killing on $[0,\infty)$. We obtain criteria for the exponential convergence to a unique quasi-stationary distribution in total…
This paper presents a conception for computing gr\"{o}bner basis. We convert some of gr\"{o}bner-computing algorithms, e.g., F5, extended F5 and GWV algorithms into a special type of algorithm. The new algorithm's finite termination problem…
Realistic modeling of ecological population dynamics requires spatially explicit descriptions that can take into account spatial heterogeneity as well as long-distance dispersal. Here, we present Monte Carlo simulations and numerical…
Assuming sufficiently many terms of a n-dimensional table defined over a field are given, we aim at guessing the linear recurrence relations with either constant or polynomial coefficients they satisfy. In many applications, the table terms…
In order to approximate the exit time of a one-dimensional diffusion process, we propose an algorithm based on a random walk. Such an algorithm so-called Walk on Moving Spheres was already introduced in the Brownian context. The aim is…
We apply the recently devised quasi-stationary simulation method to study the lifetime and order parameter of the contact process in the subcritical phase. This phase is not accessible to other methods because virtually all realizations of…
We modify the path integral representation of exciton transport in open quantum systems such that an exact description of the quantum fluctuations around the classical evolution of the system is possible. As a consequence, the time…
Recently, different dispersion strategies in population models subject to geometric catastrophes have been considered as strategies to improve the chance of po\-pu\-lation's survival. Such dispersion strategies have been contrasted with the…
This paper is concerned with a natural variant of the contact process modeling the spread of knowledge on the integer lattice. Each site is characterized by its knowledge, measured by a real number ranging from 0 = ignorant to 1 =…
The fitness of a biological strategy is typically measured by its expected reproductive rate, the first moment of its offspring distribution. However, strategies with high expected rates can also have high probabilities of extinction. A…
In this paper we discuss a closed-form approximation of the likelihood functions of an arbitrary diffusion process. The approximation is based on an exponential ansatz of the transition probability for a finite time step $\Delta t$, and a…
An approximation method is presented for probabilistic inference with continuous random variables. These problems can arise in many practical problems, in particular where there are "second order" probabilities. The approximation, based on…
In this paper we analyze a method for approximating the first-passage time density and the corresponding distribution function for a CIR process. This approximation is obtained by truncating a series expansion involving the generalized…
We consider a random walk on top of the contact process on $\mathbb{Z}^d$ with $d\geq 1$. In particular, we focus on the "contact process as seen from the random walk". Under the assumption that the infection rate of the contact process is…
We establish sufficient conditions for exponential convergence to a unique quasi-stationary distribution in the total variation norm. These conditions also ensure the existence and exponential ergodicity of the Q-process, the process…
In this paper we propose a new lifetime model, called the odd generalized exponential gompertz distribution, We obtain some of its mathematical properties. Some structural properties of the new distribution are studied. The method of…
We study bifurcations in a spatially extended nonlinear system representing population dynamics with the help of analytic calculations based on the time-independent Schr\"{o}dinger equation for a quantum particle subjected to a uniform…
Instead of using frequency dependent refractive index, we propose to use the extinction theorem to describe reflection and transmission of an ultrashort pulse passing through the boundary. When the duration of the pulse is comparable with…