Related papers: Galton-Watson processes in dynamical environments
We consider diffusion processes x_{t} on the unit interval. Doob-transformation techniques consist of a selection of x_{t}-paths procedure. The law of the transformed process is the one of a branching diffusion system of particles, each…
We analyze the long-term stability of a stochastic model designed to illustrate the adaptation of a population to variation in its environment. A piecewise-deterministic process modeling adaptation is coupled to a Feller logistic diffusion…
We explore the survival function for percolation on Galton-Watson trees. Letting $g(T,p)$ represent the probability a tree $T$ survives Bernoulli percolation with parameter $p$, we establish several results about the behavior of the random…
A class of models for large-scale evolution and mass extinctions is presented. These models incorporate environmental changes on all scales, from influences on a single species to global effects. This is a step towards a unified picture of…
Take a continuous-time Galton-Watson tree. If the system survives until a large time $T$, then choose $k$ particles uniformly from those alive. What does the ancestral tree drawn out by these $k$ particles look like? Some special cases are…
A population genetics model based on a multitype branching process, or equivalently a Galton-Watson branching process for multiple alleles, is pre- sented. The diffusion limit forward Kolmogorov equation is derived for the case of neutral…
Motivated by modeling the dynamics of a population living in a flowing medium where the environmental factors are random in space, we have studied an asymmetric variant of the one-dimensional contact process, where the quenched random…
A mass ejection model in a time-dependent random environment with both temporal and spatial correlations is introduced. When the environment has a finite correlation length, individual particle trajectories are found to diffuse at large…
We fully revisit the near soliton dynamics for the mass critical (gKdV) equation. In Part I, for a class of initial data close to the soliton, we prove that only three scenario can occur: (BLOW UP) the solution blows up in finite time $T$…
We consider a Galton-Watson process $\mathbf{Z}% (n)=(Z_{1}(n),Z_{2}(n))$ with two types of particles. Particles of type 2 may produce offspring of both types while particles of type 1 may produce particles of their own type only. Let…
We study the decay of survival probability at quantum phase transitions (QPT). The semiclassical theory is found applicable in the vicinities of critical points with infinite degeneracy. The theory predicts a power law decay of the survival…
We consider population-size-dependent branching processes (PSDBPs) which eventually become extinct with probability one. For these processes, we derive maximum likelihood estimators for the mean number of offspring born to individuals when…
We derive a thermodynamic uncertainty relation for general open quantum dynamics, described by a joint unitary evolution on a composite system comprising a system and an environment. By measuring the environmental state after the…
Let $L$ be a positive definite self-adjoint operator on the $L^2$-space associated to a $\si$-finite measure space. Let $H$ be the dual space of the domain of $L^{1/2}$ w.r.t. $L^2(\mu)$. By using an It\^o type inequality for the $H$-norm…
We introduce a branching process in a sparse random environment as an intermediate model between a Galton--Watson process and a branching process in a random environment. In the critical case we investigate the survival probability and…
Quantum systems are invariably open, evolving under surrounding influences rather than in isolation. Standard open quantum system methods eliminate all information on the environmental state to yield a tractable description of the system…
We discuss complementary recurrence and transience criteria for stochastic processes $(X_n)_{n \ge 0}$ with values in the $d$-dimensional orthant $\mathbb R^d_+$ fulfilling a non-linear stochastic equation of the form $X_{n+1}=MX_n+g(X_n)+…
In this paper, we study the speed of extinction of continuous state branching processes in subcritical L\'evy environments. More precisely, when the associated L\'evy process to the environment drifts to $-\infty$ and, under a suitable…
We study a two-dimensional process $(X, Y)$ arising as the unique nonnegative solution to a pair of stochastic differential equations driven by independent Brownian motions and compensated spectrally positive L\'evy random measures. Both…
Extinction appears ubiquitously in many fields, including chemical reactions, population biology, evolution, and epidemiology. Even though extinction as a random process is a rare event, its occurrence is observed in large finite…