Related papers: Testing Markov Chains without Hitting
Adaptive Markov chain Monte Carlo (MCMC) algorithms, which automatically tune their parameters based on past samples, have proved extremely useful in practice. The self-tuning mechanism makes them `non-Markovian', which means that their…
Expanding upon the rich history of algebraic techniques in probability, we show the existence of and construct a Markov chain using the Hopf square map on a quantum group that is both non-commutative and non-cocommutative. This extends the…
We present an approach for testing for the existence of continuous generators of discrete stochastic transition matrices. Typically, the known approaches to ascertain the existence of continuous Markov processes are based in the assumption…
We revisit the symbolic verification of Markov chains with respect to finite horizon reachability properties. The prevalent approach iteratively computes step-bounded state reachability probabilities. By contrast, recent advances in…
Despite its prevalence, probabilistic bisimilarity suffers from a lack of robustness under minuscule perturbations of the transition probabilities. This can lead to discontinuities in the probabilistic bisimilarity distance function,…
Inter-channel mis-synchronisation can be a limiting factor to the time resolution of high performance timing detectors with multiple readout channels and independent electronics units. In these systems, time calibration methods employed…
We consider the problem of characterising expected hitting times and hitting probabilities for imprecise Markov chains. To this end, we consider three distinct ways in which imprecise Markov chains have been defined in the literature: as…
In the context of Markov decision processes running in continuous time, one of the most intriguing challenges is the efficient approximation of finite horizon reachability objectives. A multitude of sophisticated model checking algorithms…
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…
We introduce the avoidance Markov metrics and theories which provide more flexibility in the design of random walk and impose new conditions on the walk to avoid (or transit) a specific node (or a set of nodes) before the stopping criteria.…
The problem of estimating an unknown discrete distribution from its samples is a fundamental tenet of statistical learning. Over the past decade, it attracted significant research effort and has been solved for a variety of divergence…
Given a probabilistic transition system (PTS) $\cal A$ partially observed by an attacker, and an $\omega$-regular predicate $\varphi$over the traces of $\cal A$, measuring the disclosure of the secret $\varphi$ in $\cal A$ means computing…
In this study, we consider sequences drawn from time-homogeneous Markov chains and introduce a novel approach for estimating first hitting-time distributions to specified terminal states. Our method- ology is based on the…
The conventional perspective on Markov chains considers decision problems concerning the probabilities of temporal properties being satisfied by traces of visited states. However, consider the following query made of a stochastic system…
Hybrid systems whose mode dynamics are governed by non-linear ordinary differential equations (ODEs) are often a natural model for biological processes. However such models are difficult to analyze. To address this, we develop a…
We consider the problem of closeness testing for two discrete distributions in the practically relevant setting of \emph{unequal} sized samples drawn from each of them. Specifically, given a target error parameter $\varepsilon > 0$, $m_1$…
Parametric Markov chains (pMC) are used to model probabilistic systems with unknown or partially known probabilities. Although (universal) pMC verification for reachability properties is known to be coETR-complete, there have been efforts…
We derive a finite-sample probabilistic bound on the parameter estimation error of a system identification algorithm for Linear Switched Systems. The algorithm estimates Markov parameters from a single trajectory and applies a variant of…
Perturbation theory for Markov chains addresses the question how small differences in the transitions of Markov chains are reflected in differences between their distributions. We prove powerful and flexible bounds on the distance of the…
Phase I distribution-free runs- and patterns-type control charts are proposed for monitoring the unknown target value (or location parameter) for both continuous and discrete individual observations. Our approach maintains the nominal…