Related papers: Periodically driven jump processes conditioned on …
Markov jump processes (or continuous-time Markov chains) are a simple and important class of continuous-time dynamical systems. In this paper, we tackle the problem of simulating from the posterior distribution over paths in these models,…
In the paper we consider some piecewise deterministic Markov process whose continuous component evolves according to semiflows, which are switched at the jump times of a Poisson process. The associated Markov chain describes the states of…
Systems with interacting degrees of freedom play a prominent role in stochastic thermodynamics. Our aim is to use the concept of detached path probabilities and detached entropy production for bipartite Markov processes and elaborate on a…
We discuss research done in two important areas of nonequilibrium statistical mechanics: fluctuation dissipation relations and dynamical fluctuations. In equilibrium systems the fluctuation-dissipation theorem gives a simple relation…
In this paper, we study a subclass of piecewise-deterministic Markov processes with a Polish state space, involving deterministic motion punctuated by random jumps that occur at exponentially distributed time intervals. Over each of these…
The reduction of a continuous Markov process with multiple metastable states to a discrete rate process is investigated in the presence of slow time dependent parameters such as periodic external forces or slowly fluctuating barrier…
The thermodynamic formalism, which was first developed for dynamical systems and then applied to discrete Markov processes, turns out to be well suited for continuous time Markov processes as well, provided the definitions are interpreted…
This article studies typical dynamics and fluctuations for a slow-fast dynamical system perturbed by a small fractional Brownian noise. Based on an ergodic theorem with explicit rates of convergence, which may be of independent interest, we…
The principal aim of the present work is to explore limit theorems for small random perturbations of a planar impulsive dynamical system, where impulses occur at hitting times of a suitable switching surface, and are thus state-dependent.…
This paper presents a nonparametric method for estimating the conditional density associated to the jump rate of a piecewise-deterministic Markov process. In our framework, the estimation needs only one observation of the process within a…
Highly-diverse ecosystems exhibit a broad distribution of population sizes and species turnover, where species at high and low abundances are exchanged over time. We show that these two features generically emerge in the fluctuating phase…
We show that the scaled cumulant generating and large deviation function, associated to a two-state Markov process involving two processes, obey a symmetry relation reminiscent of the fluctuation theorem, independent from any conditions on…
Fluctuations in small biological systems can be crucial for their function. Large-deviation theory characterizes such rare events from the perspective of stochastic processes. In most cases it is very difficult to directly determine the…
Controlling dynamical fluctuations in open quantum systems is essential both for our comprehension of quantum nonequilibrium behaviour and for its possible application in near-term quantum technologies. However, understanding these…
We consider a class of graph-valued stochastic processes in which each vertex has a type that fluctuates randomly over time. Collectively, the paths of the vertex types up to a given time determine the probabilities that the edges are…
The fluctuation theorem for entropy production is a remarkable symmetry of the distribution of produced entropy that holds universally in non-equilibrium steady states with Markovian dynamics. However, in systems with slow degrees of…
Markov Decision Processes (MDPs) have been used to formulate many decision-making problems in science and engineering. The objective is to synthesize the best decision (action selection) policies to maximize expected rewards (or minimize…
In this paper, we develop a general law of large numbers and central limit theorem for cumulative reward processes associated with finite state Markov jump processes with non-stationary transition rates. Such models commonly arise in…
Markov jump processes (MJPs) are used to model a wide range of phenomena from disease progression to RNA path folding. However, maximum likelihood estimation of parametric models leads to degenerate trajectories and inferential performance…
In this paper, we consider a subclass of piecewise deterministic Markov processes with a Polish state space that involve a deterministic motion punctuated by random jumps, occurring in a Poisson-like fashion with some state-dependent rate,…