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This paper introduces a new approach of treating platoon systems using mean-variance control formulation. The underlying system is a controlled switching diffusion in which the random switching process is a continuous-time Markov chain.…
Understanding excitation and charge transfer in disordered media is a significant challenge in chemistry, biophysics and material science. We study two experimentally-relevant measures for carriers transfer in finite-size chains, the…
We use the Markov chain approximation method to construct approximations for the solution of the mean field game (MFG) with reflecting barriers studied in Bayraktar, Budhiraja, and Cohen (2017). The MFG is formulated in terms of a…
Verification of infinite-state Markov chains is still a challenge despite several fruitful numerical or statistical approaches. For decisive Markov chains, there is a simple numerical algorithm that frames the reachability probability as…
We consider continuous-time Markov chains which display a family of wells at the same depth. We provide sufficient conditions which entail the convergence of the finite-dimensional distributions of the order parameter to the ones of a…
In this work, we present an analysis of the Burst failure effect in the $H_\infty$ norm. We present a procedure to perform an analysis between different Markov Chain models and a numerical example. In the numerical example the results…
At high levels, the asymptotic distribution of a stationary, regularly varying Markov chain is conveniently given by its tail process. The latter takes the form of a geometric random walk, the increment distribution depending on the sign of…
Process mining extracts valuable insights from event data to help organizations improve their business processes, which is essential for their growth and success. By leveraging process mining techniques, organizations gain a comprehensive…
We develop a model for credit rating migration that accounts for the impact of economic state fluctuations on default probabilities. The joint process for the economic state and the rating is modelled as a time-homogeneous Markov chain.…
This paper aims to derive a quantitative model to evaluate the impact of information flow on the effectiveness of disaster response. At the core of the model is a specialized absorbing Markov chain that models the process of delivering…
We present a novel algorithm to solve a non-linear system of equations, whose solution can be interpreted as a tight lower bound on the vector of expected hitting times of a Markov chain whose transition probabilities are only partially…
We use the mean exit time to quantify macroscopic dynamical behaviors of stochastic dynamical systems driven by tempered L\'evy fluctuations, which are solutions of nonlocal elliptic equations. Firstly, we construct a new numerical scheme…
Motivated by a real failure dataset in a two-dimensional context, this paper presents an extension of the Markov modulated Poisson process (MMPP) to two dimensions. The one-dimensional MMPP has been proposed for the modeling of dependent…
In a specific class of open quantum systems with finite and fixed numbers of collapsed quantum states, the semi-Markov process method is used to calculate the large deviations of the first passage time statistics. The core formula is an…
Monte Carlo algorithms simulate some prescribed number of samples, taking some random real time to complete the computations necessary. This work considers the converse: to impose a real-time budget on the computation, which results in the…
The Rate of Occurrence of Failures (ROCOF) is a widely utilized indicator for assessing a system's performance over time, yet it does not fully disclose the instantaneous behavior of a system. This paper introduces new measures to…
We address the problem of community detection in networks by introducing a general definition of Markov stability, based on the difference between the probability fluxes of a Markov chain on the network at different time scales. The…
In Markov networks, measurement blackouts with unknown frequency compromise observations such that thermodynamic quantities can no longer be inferred reliably. In particular, the observed currents neither discern equilibrium from…
We consider a Markov chain $(M_{n})_{n\ge 0}$ on the set $\mathbb{N}_{0}$ of nonnegative integers which is eventually decreasing, i.e. $\mathbb{P}\{M_{n+1}<M_{n}|M_{n}\ge a\}=1$ for some $a\in\mathbb{N}$ and all $n\ge 0$. We are interested…
Markov chain Monte Carlo is a method of producing a correlated sample in order to estimate features of a target distribution via ergodic averages. A fundamental question is when should sampling stop? That is, when are the ergodic averages…