Related papers: Maximal Sensitive Dependence and the Optimal Path …
Systems that evolve towards a state from which they cannot depart are common in nature. But the fluctuation-dissipation theorem, a fundamental result in statistical mechanics, is mainly restricted to systems near-stationarity. In processes…
Realistic models of biological processes typically involve interacting components on multiple scales, driven by changing environment and inherent stochasticity. Such models are often analytically and numerically intractable. We revisit a…
We consider stationary stochastic processes arising from dynamical systems by evaluating a given observable along the orbits of the system. We focus on the extremal behaviour of the process, which is related to the entrance in certain…
We consider a branching Markov process in continuous time in which the particles evolve independently as spectrally negative L\'evy processes. When the branching mechanism is critical or subcritical, the process will eventually die and we…
This work is devoted to the investigation of the most probable transition time between metastable states for stochastic dynamical systems. Such a system is modeled by a stochastic differential equation with non-vanishing Brownian noise, and…
Population extinction is a rare event which requires overcoming an effective barrier. We show that the extinction rate can be fragile: a small change in the system parameters leads to an exponentially strong change of the rate, with the…
Certain Markov processes, or deterministic evolution equations, have the property that they are dual to a stochastic process that exhibits extinction versus unbounded growth, i.e., the total mass in such a process either becomes zero, or…
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…
Exit paths in buildings are designed to minimise evacuation time when the building is at full capacity. We present an evacuation support system which does this regardless of the number of evacuees. The core concept is to even-out congestion…
Recently path integral methods have been developed for stochastic optimal control for a wide class of models with non-linear dynamics in continuous space-time. Path integral methods find the control that minimizes the expected cost-to-go.…
In this paper we study the diffusion of an SIS-type epidemics on a network under the presence of a random environment, that enters in the definition of the infection rates of the nodes. Accordingly, we model the infection rates in the form…
We study a stochastic SIS (susceptible-infected-susceptible) epidemic dynamics on network, under the effect of a Markovian regime-switching. We first prove the existence of a unique global positive solution, and find a positive invariant…
We provide a complete characterization of optimal extinction in a two-sector model of economic growth through three results, surprising in both their simplicity and intricacy. (i) When the discount factor is below a threshold identified by…
A class of models is introduced describing the evolution of population species whose carrying capacities are functionals of these populations. The functional dependence of the carrying capacities reflects the fact that the correlations…
We model an epidemic where the per-person infectiousness in a network of geographic localities changes with the total number of active cases. This would happen as people adopt more stringent non-pharmaceutical precautions when the…
We study time continuous branching processes with exponentially distributed lifetimes, with two types of cells that proliferate according to binary fission. A range of possible system dynamics are considered, each of which is characterized…
In this paper, we investigate the asymptotic behaviors of the survival probability and maximal displacement of a subcritical branching killed L\'{e}vy process $X$ in $\mathbb{R}$. Let $\zeta$ denote the extinction time, $M_t$ be the maximal…
Populations of competing biological species exhibit a fascinating interplay between the nonlinear dynamics of evolutionary selection forces and random fluctuations arising from the stochastic nature of the interactions. The processes…
We propose a model of multispecies populations surviving on distributed resources. System dynamics are investigated under changes in abiotic factors such as the climate, as parameterized through environmental temperature. In particular, we…
In stochastic resonance, a periodically forced Brownian particle in a double-well potential jumps between minima at rare increments, the prediction of which poses a major theoretical challenge. Here, we use a path-integral method to find a…