Related papers: Probability measures on graph trajectories
We describe an exact approach for calculating transition probabilities and waiting times in finite-state discrete-time Markov processes. All the states and the rules for transitions between them must be known in advance. We can then…
We study continuous-time Markov chains on the non-negative integers under mild regularity conditions (in particular, the set of jump vectors is finite and both forward and backward jumps are possible). Based on the so-called flux balance…
We introduce a general class of distances (metrics) between Markov chains, which are based on linear behaviour. This class encompasses distances given topologically (such as the total variation distance or trace distance) as well as by…
Probability models on graphs are becoming increasingly important in many applications, but statistical tools for fitting such models are not yet well developed. Here we propose a general method of moments approach that can be used to fit a…
We study inhomogeneous continuous-time weakly ergodic Markov chains with a finite state space. We introduce the notion of a Markov chain with the regular structure of an infinitesimal matrix and study the sharp upper bounds on the rate of…
Computing the probability of evidence even with known error bounds is NP-hard. In this paper we address this hard problem by settling on an easier problem. We propose an approximation which provides high confidence lower bounds on…
. Markov chains in time, such as simple random walks, are at the heart of probability. In space, due to the absence of an obvious definition of past and future, a range of definitions of Markovianity have been proposed. In this paper, after…
We study a class of Markov chains that model the evolution of a quantum system subject to repeated measurements. Each Markov chain in this class is defined by a measure on the space of matrices. It is then given by a random product of…
Subject of this letter is the dynamics of a chain obtained performing the continuous limit of a system of links and beads. In particular, the probability distribution of the relative position between two points of the chain averaged over a…
The paper studies a probabilistic notion of causes in Markov chains that relies on the counterfactuality principle and the probability-raising property. This notion is motivated by the use of causes for monitoring purposes where the aim is…
This paper integrates two strands of the literature on stability of general state Markov chains: conventional, total variation based results and more recent order-theoretic results. First we introduce a complete metric over Borel…
Probabilistic model checking for systems with large or unbounded state space is a challenging computational problem in formal modelling and its applications. Numerical algorithms require an explicit representation of the state space, while…
We consider the higher-order Markov Chain, and characterize the second order Markov chains admitting every probability distribution vector as a stationary vector. The result is used to construct Markov chains of higher-order with the same…
Markov chains are a convenient means of generating realizations of networks, since they require little more than a procedure for rewiring edges. If a rewiring procedure exists for generating new graphs with specified statistical properties,…
For a stochastically monotone Markov chain taking values in a Polish space, we present a number of conditions for existence and for uniqueness of its stationary regime, as well as for closeness of its transient trajectories. In particular,…
We study approximations of evolving probability measures by an interacting particle system. The particle system dynamics is a combination of independent Markov chain moves and importance sampling/resampling steps. Under global regularity…
We present a method to sample Markov-chain trajectories constrained to both the initial and final conditions, which we term Markov bridges. The trajectories are conditioned to end in a specific state at a given time. We derive the master…
An algorithm for estimating quasi-stationary distribution of finite state space Markov chains has been proven in a previous paper. Now this paper proves a similar algorithm that works for general state space Markov chains under very general…
We propose a Markov chain simulation method to generate simple connected random graphs with a specified degree sequence and level of clustering. The networks generated by our algorithm are random in all other respects and can thus serve as…
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…