Related papers: Numerical Aspects of Computing Possible Equilibria…
The paper studies a class of critical Markov branching processes with infinite variance of the offspring distribution. The processes admit also an immigration component at the jump-points of a non-homogeneous Poisson process, assuming that…
We prove stable convergence of conditional least squares estimators of drift parameters for supercritical continuous state and continuous time branching processes with immigration based on discrete time observations.
We provide a simple set of sufficient conditions for the weak convergence of discrete Galton-Watson branching processes with immigration to continuous time and continuous state branching processes with immigration.
An Allee effect occurs when the per-capita growth rate increases at low densities. Here, we investigate the evolutionary stability of a partial migration population with migrant population experiencing Allee effects. Partial migration is a…
We propose a framework for studying predictability of extreme events in complex systems. Major conceptual elements -- hierarchical structure, spatial dynamics, and external driving -- are combined in a classical branching diffusion with…
Robustness is often regarded as a critical future challenge for real-world applications, where stability is essential. However, as models often learn tasks in a similar order, we hypothesize that easier tasks will be easier regardless of…
We consider a broad class of continuous-time two-type population size-dependent Markov Branching Processes. The offspring distribution can depend on the current (alive) and total (dead and alive) populations. Using stochastic approximation…
Whether in search of better trade opportunities or escaping wars, humans have always been on the move. For almost a century, mathematical models of human mobility have been instrumental in the quantification of commuting patterns and…
We focus on the partial sum $S_{n}=X_{1}+\cdots+X_{n}$ of the critical branching process with immigration $\{X_{n}\}$, when the offspring $\xi$ is regularly varying with index $\nu+1$ and the immigration $\eta$ is regularly varying with…
The dynamics of adaptation is difficult to predict because it is highly stochastic even in large populations. The uncertainty emerges from number fluctuations, called genetic drift, arising in the small number of particularly fit…
We study the performance of general dynamic matching models. This model is defined by a connected graph, where nodes represent the class of items and the edges the compatibilities between items. Items of different classes arrive one by one…
We report that population dynamics in fluctuating environment accompanies mathematically equivalent structure to steady state thermodynamics. By employing the structure, population growth in fluctuating environment is decomposed into…
In this paper, we design two chapters to discuss trade dynamics with heterogeneous fluctuations, contributing new insights to macroeconomic issues related to international trade. In the first chapter, we model general exchange rate…
The notion of stability can be generalised to point processes by defining the scaling operation in a randomised way: scaling a configuration by $t$ corresponds to letting such a configuration evolve according to a Markov branching particle…
In this article we focus on the partial sum $S_{n}=X_{1}+\cdots+X_{n}$ of the subcritical branching process with immigration $\{X_{n}\}_{n\in\mathbb{N_{+}}}$, under the condition that one of the offspring $\xi$ or immigration $\eta$ is…
Finding a good compromise between the exploitation of known resources and the exploration of unknown, but potentially more profitable choices, is a general problem, which arises in many different scientific disciplines. We propose a…
Understanding and predicting human migration patterns is a central challenge in population dynamics research. Traditional physics-inspired gravity and radiation models represent migration flows as functions of attractiveness using…
Continuous state branching processes with immigration are studied. We are particularly concerned with the associated (non-symmetric) Dirichlet form. After observing that gamma distributions are only reversible distributions for this class…
Over the last two decades, several methods have been proposed for stabilizing the dynamics of biological populations. However, these methods have typically been evaluated using different population dynamics models and in the context of very…
Consider a branching process $\{Z_n\}_{n\ge 0}$ with immigration in varying environment. For $a\in\{0,1,2,...\},$ let $C=\{n\ge0:Z_n=a\}$ be the collection of times at which the population size of the process attains level $a.$ We give a…