Related papers: Are Parametric Markov Chains Monotonic?
The limiting probability distribution is one of the key characteristics of a Markov chain since it shows its long-term behavior. In this paper, for a higher order Markov chain, we establish some properties related to its exact limiting…
Markov chains and Markov decision processes (MDPs) are well-established probabilistic models. While finite Markov models are well-understood, analysing their infinite counterparts remains a significant challenge. Decisiveness has proven to…
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…
We develop a general theory of Markov chains realizable as random walks on $\mathscr R$-trivial monoids. It provides explicit and simple formulas for the eigenvalues of the transition matrix, for multiplicities of the eigenvalues via…
We investigate the impact of spontaneous movement in the complexity of verification problems for an automata-based protocol model of networks with selective broadcast communication. We first consider reachability of an error state and show…
In this paper, we seek to understand the behavior of dynamical systems that are perturbed by a parameter that changes discretely in time. If we impose certain conditions, we can study certain embedded systems within a hybrid system as…
In this work, we characterise the statistics of Markov chains by constructing an associated sequence of periodic differential operators. Studying the density of states of these operators reveals the absolutely continuous invariant measure…
We introduce a simple approach for testing the reliability of homogeneous generators and the Markov property of the stochastic processes underlying empirical time series of credit ratings. We analyze open access data provided by Moody's and…
In this paper we study various properties of finite stochastic systems or hidden Markov chains as they are alternatively called. We discuss their construction following different approaches and we also derive recursive filtering formulas…
We introduce a Markov chain model of concurrent quantum programs. This model is a quantum generalization of Hart, Sharir and Pnueli's probabilistic concurrent programs. Some characterizations of the reachable space, uniformly repeatedly…
Parametric Markov chains (pMCs) are Markov chains (MCs) with symbolic probabilities. A pMC encodes a family of MCs, where each member is obtained by replacing parameters with constants. The parameters allow encoding dependencies between…
This paper is concerned with the development of rigorous approximations to various expectations associated with Markov chains and processes having non-stationary transition probabilities. Such non-stationary models arise naturally in…
We consider the problem of finding the Perron-Frobenius eigenvector of a primitive matrix. Dividing each of the rows of the matrix by the sum of the elements in the row, the resulting new matrix is stochastic. We give a formula for the…
Inferring the causal structure that links n observables is usually based upon detecting statistical dependences and choosing simple graphs that make the joint measure Markovian. Here we argue why causal inference is also possible when only…
We present a method to overapproximate forward stochastic reach sets of discrete-time, stochastic nonlinear systems with interval geometry. This is made possible by extending the theory of mixed-monotone systems to incorporate stochastic…
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…
We establish a simple variance inequality for U-statistics whose underlying sequence of random variables is an ergodic Markov Chain. The constants in this inequality are explicit and depend on computable bounds on the mixing rate of the…
This paper considers large families of Markov chains (MCs) that are defined over a set of parameters with finite discrete domains. Such families occur in software product lines, planning under partial observability, and sketching of…
We present a system for online probabilistic event forecasting. We assume that a user is interested in detecting and forecasting event patterns, given in the form of regular expressions. Our system can consume streams of events and forecast…
In this paper, we present a methodology to estimate the parameters of stochastically contaminated models under two contamination regimes. In both regimes, we assume that the original process is a variable length Markov chain that is…