Related papers: Spatial birth and death processes as solutions of …
We consider excursions for a class of stochastic processes describing a population of discrete individuals experiencing density-limited growth, such that the population has a finite carrying capacity and behaves qualitatively like the…
A master equation for the evolution of two-dimensional universe is derived based on the simplicial quantum gravity regarding the evolution as the Markov process of a space-time lattice. Three typical phases, expanding, elongating and…
Spatial systems with heterogeneities are ubiquitous in nature, from precipitation, temperature and soil gradients controlling vegetation growth to morphogen gradients controlling gene expression in embryos. Such systems, generally described…
In biology and ecology, individuals or communities of individuals living in unpredictable environments often alternate between different evolutionary strategies to spread and reduce risks. Such behavior is commonly referred to as…
This paper constructs a solvability theory for a system of stochastic partial differential equations. On account of the Kolmogorov continuity theorem, solutions are looked for in certain H\"older-type classes in which a random field is…
We consider a generalized birth-death process (GBDP) whose state space is a finite subset of a $q$-dimensional lattice. It is assumed that there can be a jump of finite step size in all possible directions such that the probability of…
The generation of random spatial data on a computer is an important tool for understanding the behavior of spatial processes. In this paper we describe how to generate realizations from the main types of spatial processes, including…
We study conservative particle systems on W^S, where S is countable and W = {0, ..., N} or the natural numbers. The rate of a particle moving from site x to site y is given by p(x,y) b(eta_x, eta_y), where eta_z is the number of particles…
We propose a new class of parameterizations for spatio-temporal point processes which leverage Neural ODEs as a computational method and enable flexible, high-fidelity models of discrete events that are localized in continuous time and…
Standard evolutionary theories of aging and mortality, implicitly based on assumptions of spatial averaging, hold that natural selection cannot favor shorter lifespan without direct compensating benefit to individual reproductive success.…
In this paper, we review recent results of ours concerning branching processes with general lifetimes and neutral mutations, under the infinitely many alleles model, where mutations can occur either at birth of individuals or at a constant…
We introduce the notion of birth and death cochains as generalized versions of birth and death simplices in persistent cohomology. We show that birth and death cochains (unlike birth and death simplices) are always unique for a given…
This chapter provides a pedagogical introduction and overview of spatial and temporal correlation and fluctuation effects resulting from the fundamentally stochastic kinetics underlying chemical reactions and the dynamics of populations or…
Stochastic homogenization is achieved for a class of elliptic and parabolic equations describing the lifetime, in large domains, of stationary diffusion processes in random environment which are small, statistically isotropic perturbations…
Topological entropy or spatial entropy is a way to measure the complexity of shift spaces. This study investigates the relationships between the spatial entropy and the various periodic entropies which are computed by skew-coordinated…
Delay is an important and ubiquitous aspect of many biochemical processes. For example, delay plays a central role in the dynamics of genetic regulatory networks as it stems from the sequential assembly of first mRNA and then protein.…
A stochastic ordering approach is applied with Stein's method for approximation by the equilibrium distribution of a birth-death process. The usual stochastic order and the more general s-convex orders are discussed. Attention is focused on…
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…
We consider Markov processes that alternate continuous motions and jumps in a general locally compact polish space. Starting from a mechanistic construction, a first contribution of this article is to provide conditions on the dynamics so…
We study ergodic properties of a class of Markov-modulated general birth-death processes under fast regime switching. The first set of results concerns the ergodic properties of the properly scaled joint Markov process with a parameter that…