Related papers: Occupation times via Bessel functions
We consider multi-state capture-recapture-recovery data where observed individuals are recorded in a set of possible discrete states. Traditionally, the Arnason-Schwarz model has been fitted to such data where the state process is modeled…
Many natural and engineered systems can be modeled as discrete state Markov processes. Often, only a subset of states are directly observable. Inferring the conditional probability that a system occupies a particular hidden state, given the…
We introduce a discrete time microscopic single particle model for kinetic transport. The kinetics is modeled by a two-state Markov chain, the transport by deterministic advection plus a random space step. The position of the particle after…
The mean time taken by an irreducible Markov chain on a finite state space to hit a target chosen at random according to the stationary distribution does not depend on the initial state of the chain. This mean time is known as Kemeny's…
We consider additive functionals of Markov processes in continuous time with general (metric) state spaces. We derive concentration bounds for their exponential moments and moments of finite order. Applications include diffusions,…
The charge transport properties of zero-temperature multi-orbital quantum dot systems with one dot coupled to leads and the other dots coupled only capacitatively are studied within density functional theory. It is shown that the setup is…
We study the symmetric simple exclusion process with Glauber dynamics. When the process starts from a nonequilibrium measure, we prove central limit theorems for the occupation time in dimension two, and sample path moderate deviation…
Limit theorems are presented for the rescaled occupation time fluctuation process of a critical finite variance branching particle system in $\mathbb{R}^{d}$ with symmetric $\alpha$-stable motion starting off from either a standard Poisson…
Markov processes with stochastic resetting towards the origin generically converge towards non-equilibrium steady-states. Long dynamical trajectories can be thus analyzed via the large deviations at Level 2.5 for the joint probability of…
The strong $L^2$-approximation of occupation time functionals is studied with respect to discrete observations of a $d$-dimensional c\`adl\`ag process. Upper bounds on the error are obtained under weak assumptions, generalizing previous…
Trapped ions naturally host multiple motional modes alongside long-lived spin qubits, providing a scalable multimode bosonic register. Efficiently characterizing such bosonic registers requires the ability to access many motional modes with…
We present a proposal of a set-up to measure the work distribution due to an arbitrary unitary process acting on the spatial transverse degrees of freedom of a light beam. Hermite-Gaussian optical modes representing a quantum harmonic…
How to understand the order of Floquet stationary states in the presence of external bath coupling and their statistical mechanics is challenging; the answers are important for preparations and control of those Floquet states. Here, we…
We establish limit theorems for re-scaled occupation time fluctuations of a sequence of branching particle systems in $\R^d$ with anisotropic space motion and weakly degenerate splitting ability. In the case of large dimensions, our limit…
We derive expressions for the dispersion for two classes of random variables in Markov processes. Random variables like current and activity pertain to the first class, which is composed by random variables that change whenever a jump in…
We study the joint moments of occupation times on the legs of a diffusion spider. Specifically, we give a recursive formula for the Laplace transform of the joint moments, which extends earlier results for a one-dimensional diffusion. For a…
We consider an absorbing Markov decision process with Borel state and action spaces. We study conditions under which the MDP is uniformly absorbing and the set of occupation measures of the MDP is compact in the usual weak topology. These…
We consider a class of stochastic dynamical systems, called piecewise deterministic Markov processes, with states $(x, \s)\in \O\times \G$, $\O$ being a region in $\bbR^d$ or the $d$--dimensional torus, $\G$ being a finite set. The…
Mechanistic modelling of animal movement is often formulated in discrete time despite problems with scale invariance, such as handling irregularly timed observations. A natural solution is to formulate in continuous time, yet uptake of this…
Random walks are a fundamental model in applied mathematics and are a common example of a Markov chain. The limiting stationary distribution of the Markov chain represents the fraction of the time spent in each state during the stochastic…