Related papers: Statistical dynamics of continuous systems: pertur…
Markov models are widely used to describe processes of stochastic dynamics. Here, we show that Markov models are a natural consequence of the dynamical principle of Maximum Caliber. First, we show that when there are different possible…
The stochastic growth-fragmentation model describes the temporal evolution of a structured cell population through a discrete-time and continuous-state Markov chain. The simulations of this stochastic process and its invariant measure are…
The paper is largely of a review nature. It considers two main methods used to study stability and obtain appropriate quantitative estimates of perturbations of (inhomogeneous) Markov chains with continuous time and a finite or countable…
The concepts of probability, statistics and stochastic theory are being successfully used in structural engineering. Markov Chain modelling is a simple stochastic process model that has found its application in both describing stochastic…
A Kawasaki dynamics in continuum is a dynamics of an infinite system of interacting particles in $\mathbb{R}^d$ which randomly hop over the space. In this paper, we deal with an equilibrium Kawasaki dynamics which has a Gibbs measure $mu$…
A calculational approach in fluid turbulence is presented. Use is made of the attracting nature of the fluid-dynamic dynamical system. An approximate approach is offerred that effectively propagates the statistics in time. Loss of…
Two coupled spatial birth-and-death Markov evolutions on $\mathbb{R}^d$ are obtained as unique weak solutions to the associated Fokker-Planck equations. Such solutions are constructed by its associated sequence of correlation functions…
We consider Vlasov-type scaling for the Glauber dynamics in continuum with a positive integrable potential, and construct rescaled and limiting evolutions of correlation functions. Convergence to the limiting evolution for the positive…
This paper considers a simulation-based estimator for a general class of Markovian processes and explores some strong consistency properties of the estimator. The estimation problem is defined over a continuum of invariant distributions…
We study a class of multi-stage stochastic programs, which incorporate modeling features from Markov decision processes (MDPs). This class includes structured MDPs with continuous action and state spaces. We extend policy graphs to include…
We formulate some simple conditions under which a Markov chain may be approximated by the solution to a differential equation, with quantifiable error probabilities. The role of a choice of coordinate functions for the Markov chain is…
Graphical Markov models combine conditional independence constraints with graphical representations of stepwise data generating processes.The models started to be formulated about 40 years ago and vigorous development is ongoing.…
We present a stochastic model of population dynamics exploiting cross-sectional data in trend analysis and forecasts for groups and cohorts of a population. While sharing the convenient features of classic Markov models, it alleviates the…
High-dimensional dynamical systems projected onto a reduced-order model cease to be deterministic and are best described by probability distributions in state space. Their equations of motion map onto an evolution operator with a…
Model reduction of Markov processes is a basic problem in modeling state-transition systems. Motivated by the state aggregation approach rooted in control theory, we study the statistical state compression of a discrete-state Markov chain…
In the paper we consider a stochastic model which called Markov Q-processes that forms a continuous-time Markov population system. Markov Q-processes are defined as stochastic Markov branching processes with trajectories continuing in the…
There has been an increasing demand for formal methods in the design process of safety-critical synthetic genetic circuits. Probabilistic model checking techniques have demonstrated significant potential in analyzing the intrinsic…
Understanding the stability and long-time behavior of generative models is a fundamental problem in modern machine learning. This paper provides quantitative bounds on the sampling error of score-based generative models by leveraging…
Many spatio-temporal data record the time of birth and death of individuals, along with their spatial trajectories during their lifetime, whether through continuous-time observations or discrete-time observations. Natural applications…
We propose a probabilistic framework for developing computational models of biological neural systems. In this framework, physiological recordings are viewed as discrete-time partial observations of an underlying continuous-time stochastic…