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Monte Carlo simulations of systems of particles such as hard spheres or soft spheres with singular kernels can display around a phase transition prohibitively long convergence times when using traditional Hasting-Metropolis reversible…
In this paper, we study discrete-time absorbing Markov Decision Processes (MDP) with measurable state space and Borel action space with a given initial distribution. For such models, solutions to the characteristic equation that are not…
We propose a class of continuous-time Markov counting processes for analyzing correlated binary data and establish a correspondence between these models and sums of exchangeable Bernoulli random variables. Our approach generalizes many…
We consider a priori estimates of possibly sign-changing solutions to superlinear parabolic problems and their applications (blow-up rates, energy blow-up, continuity of blow-up time, existence of nontrivial steady states etc). Our…
We develop a new algorithm for scheduling the charging process of a large number of electric vehicles (EVs) over a finite horizon. We assume that EVs arrive at the charging stations with different charge levels and different flexibility…
With the growing popularity of electric vehicles as a means of addressing climate change, concerns have emerged regarding their impact on electric grid management. As a result, predicting EV charging demand has become a timely and important…
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…
This paper considers environmental problems of natural and anthropogenic atmospheric aerosol pollution and its global and regional monitoring. Efficient aerosol investigations may be achieved by spectropolarimetric measurements.…
In present paper we suggest a new universal approach to study complex systems by microscopic, mesoscopic and macroscopic methods. We discuss new possibilities of extracting information on nonstationarity, unsteadiness and non-Markovity of…
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,…
We derive explicit integrability conditions for stochastic integrals taken over time and space driven by a random measure. Our main tool is a canonical decomposition of a random measure which extends the results from the purely temporal…
A classical problem for Markov chains is determining their stationary (or steady-state) distribution. This problem has an equally classical solution based on eigenvectors and linear equation systems. However, this approach does not scale to…
We present a dynamical framework for modeling the motion of point-like charged particles, with or without mass, in general external electromagnetic fields. A key feature of this formulation is the treatment of time coordinate as a dynamical…
For a class of piecewise deterministic Markov processes we introduce a stochastic calculus which is a certain non-Gaussian counterpart to the classical Malliavin calculus. As an application we investigate the regularity of densities of…
We consider classical electromagnetic systems in which the current density ${\bf J}$ does not change with time, but has nonzero divergence, so that electric charge does build up steadily over time. We show that for such a system, the…
This paper presents a self-contained account for coupling arguments and applications in the context of Markov processes. We first use coupling to describe the transport problem, which leads to the concepts of optimal coupling and…
Markov automata combine non-determinism, probabilistic branching, and exponentially distributed delays. This compositional variant of continuous-time Markov decision processes is used in reliability engineering, performance evaluation and…
We consider a general honest homogeneous continuous-time Markov process with restarts. The process is forced to restart from a given distribution at time moments generated by an independent Poisson process. The motivation to study such…
We report guiding and manipulation of charged particle beams by means of electrostatic optics based on a principle similar to the electrodynamic Paul trap. We use hundreds of electrodes fabricated on planar substrates and supplied with…
We study the mobility of a charged colloidal particle in a constant homogeneous electric field by means of computer simulations. The simulation method combines a lattice Boltzmann scheme for the fluid with standard Langevin dynamics for the…