Related papers: Occupancy times for time-dependent stage-structure…
A semi-Markov process is one that changes states in accordance with a Markov chain but takes a random amount of time between changes. We consider the generalisation to semi-Markov processes of the classical Lamperti law for the occupation…
This study of occupation time densities for continuous-time Markov processes was inspired by the work of E.Nir et al (2006) in the field of Single Molecule FRET spectroscopy. There, a single molecule fluctuates between two or more states,…
Occupancy processes are a broad class of discrete time Markov chains on $\{0,1\}^{n}$ encompassing models from diverse areas. This model is compared to a collection of $n$ independent Markov chains on $\{0,1\}$, which we call the…
We present a systematic study of the statistics of the occupation time and related random variables for stochastic processes with independent intervals of time. According to the nature of the distribution of time intervals, the probability…
This paper introduces a linear state-space model with time-varying dynamics. The time dependency is obtained by forming the state dynamics matrix as a time-varying linear combination of a set of matrices. The time dependency of the weights…
The goal of this article is to contribute towards the conceptual and quantitative understanding of the evolutionary benefits for (microbial) populations to maintain a seed bank (consisting of dormant individuals) when facing fluctuating…
Occupancy models are used in statistical ecology to estimate species dispersion. The two components of an occupancy model are the detection and occupancy probabilities, with the main interest being in the occupancy probabilities. We show…
We obtain the fluctuations for the occupation time of one-dimensional symmetric exclusion processes with speed change, where the transition rates (conductances) are driven by a general function W. The approach does not require sharp bounds…
How does a driven system with many energy levels approach its steady state? Insights are gained by studying a system with three energy levels when the ground state is excited by a laser. The time-dependent occupation probabilities of the…
The need to model a Markov renewal on-off process with multiple off-states arise in many applications such as economics, physics, and engineering. Characterization of the occupation time of one specific off-state marginally or two…
We consider the occupation area of spherical (fractional) Brownian motion, i.e. the area where the process is positive, and show that it is uniformly distributed. For the proof, we introduce a new simple combinatorial view on occupation…
In this short communication we study a fluid queue with a finite buffer. The performance measure we are interested in is the occupation time over a finite time period, i.e., the fraction of time the workload process is below some fixed…
The time which a diffusing particle spends in a certain region of space is known as the occupation time, or the residence time. Recently the joint occupation time statistics of an ensemble of non-interacting particles was addressed using…
Dormancy is a widespread adaptive strategy that enables populations to persist in fluctuating environments, yet how its benefits depend on the temporal structure of environmental variability remains unclear. We examine how dormancy…
Human travelling behaviours are markedly regular, to a large extent, predictable, and mostly driven by biological necessities (\eg sleeping, eating) and social constructs (\eg school schedules, synchronisation of labour). Not surprisingly,…
We investigate the distribution of occupation times for a particle undergoing a random walk among random energy traps and in the presence of a deterministic potential field $U^{{\rm det}}(x)$. When the distribution of energy traps is…
The transition between low and high density phases is a typical feature of systems with social interactions. This contribution focuses on simple evacuation design of one room with one entrance and one exit; four passing-through experiments…
A Markov process fluctuating away from its typical behavior can be represented in the long-time limit by another Markov process, called the effective or driven process, having the same stationary states as the original process conditioned…
The environment in which a population evolves can have a crucial impact on selection. We study evolutionary dynamics in finite populations of fixed size in a changing environment. The population dynamics are driven by birth and death…
Cellular differentiation and evolution are stochastic processes that can involve multiple types (or states) of particles moving on a complex, high-dimensional state-space or "fitness" landscape. Cells of each specific type can thus be…