Related papers: Distance Reducing Markov Bases
This paper studies the last-column-block-augmented northwest-corner truncation (LC-block-augmented truncation, for short) of discrete-time block-monotone Markov chains under subgeometric drift conditions. The main result of this paper is to…
Imprecise continuous-time Markov chains are a robust type of continuous-time Markov chains that allow for partially specified time-dependent parameters. Computing inferences for them requires the solution of a non-linear differential…
We prove an upper bound on the total variation mixing time of a finite Markov chain in terms of the absolute spectral gap and the number of elements in the state space. Unlike results requiring reversibility or irreducibility, this bound is…
In this work, we focus on the stationary analysis of a specific class of continuous time Markov-modulated reflected random walks in the quarter plane with applications in the modelling of two-node Markov-modulated queueing networks with…
In this work, we consider an inhomogeneous (discrete time) Markov chain and are interested in its long time behavior. We provide sufficient conditions to ensure that some of its asymptotic properties can be related to the ones of a…
We present a permutation-invariant distance between atomic configurations, defined through a functional representation of atomic positions. This distance enables to directly compare different atomic environments with an arbitrary number of…
We study the asymptotic properties, in the weak sense, of regenerative processes and Markov renewal processes. For the latter, we derive both renewal-type results, also concerning the related counting process, and ergodic-type ones,…
We exhibit an efficient procedure for testing, based on a single long state sequence, whether an unknown Markov chain is identical to or $\varepsilon$-far from a given reference chain. We obtain nearly matching (up to logarithmic factors)…
We develop a theory of weak Poincar\'e inequalities to characterize convergence rates of ergodic Markov chains. Motivated by the application of Markov chains in the context of algorithms, we develop a relevant set of tools which enable the…
Consider a discrete time, ergodic Markov chain with finite state space which is started from stationarity. Fill and Lyzinski (2014) showed that, in some cases, the hitting time for a given state may be represented as a sum of a geometric…
The Euclidean distance geometry problem arises in a wide variety of applications, from determining molecular conformations in computational chemistry to localization in sensor networks. When the distance information is incomplete, the…
We review the relations between distance matrices and isometric embeddings and give simple proofs that distance matrices defined on euclidean and spherical spaces have all eigenvalues except one non-negative. Several generalizations are…
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…
A derivation of the properties of pulsed radiative imaging systems is presented with examples drawn from conventional, synthetic aperture, and interferometric radar. A geometric construction of the space and time components of a radar…
Lifted Markov chains are Markov chains on graphs with added local "memory" and can be used to mix towards a target distribution faster than their memoryless counterparts. Upper and lower bounds on the achievable performance have been…
To avoid poor empirical performance in Metropolis-Hastings and other accept-reject-based algorithms practitioners often tune them by trial and error. Lower bounds on the convergence rate are developed in both total variation and Wasserstein…
Identifiability, and the closely related idea of partial smoothness, unify classical active set methods and more general notions of solution structure. Diverse optimization algorithms generate iterates in discrete time that are eventually…
We study time-changed Markov processes to speed up the convergence of Markov chain Monte Carlo (MCMC) algorithms. The time-changed process is defined by adjusting the speed of time of a base process via a user-chosen, state-dependent…
Hybrid stochastic differential equations are a useful tool to model continuously varying stochastic systems which are modulated by a random environment that may depend on the system state itself. In this paper, we establish the pathwise…
Behavioural distances provide a robust alternative to notions of equivalence such as bisimilarity in the context of probabilistic transition systems. They can be defined as least fixed points, whose universal property allows us to exhibit…