Related papers: Computing performability measures in Markov chains…
We study the induced measure obtained from a 1-step Markov measure, supported by a topological Markov chain, after the mapping of the original alphabet onto another one. We give sufficient conditions for the induced measure to be a Gibbs…
Two approaches to studying the correlation functions of the binary Markov sequences are considered. The first of them is based on the study of probability of occurring different ''words'' in the sequence. The other one uses recurrence…
This paper is concerned with the study of the stability of dynamical systems evolving on time scales. We first {formalize the notion of matrix measures on time scales, prove some of their key properties and make use of this notion to study…
The concept of signature is a useful tool in the analysis of semicoherent systems with continuous and i.i.d. component lifetimes, especially for the comparison of different system designs and the computation of the system reliability. For…
Strong and weak simulation relations have been proposed for Markov chains, while strong simulation and strong probabilistic simulation relations have been proposed for probabilistic automata. However, decision algorithms for strong and weak…
The evaluation of a matrix exponential function is a classic problem of computational linear algebra. Many different methods have been employed for its numerical evaluation [Moler C and van Loan C 1978 SIAM Review 20 4], none of which…
We propose a very fast approximate Markov Chain Monte Carlo (MCMC) sampling framework that is applicable to a large class of sparse Bayesian inference problems, where the computational cost per iteration in several models is of order…
Functional inequalities such as the Poincar\'e and log-Sobolev inequalities quantify convergence to equilibrium in continuous-time Markov chains by linking generator properties to variance and entropy decay. However, many applications,…
Statistical machine learning often uses probabilistic algorithms, such as Markov Chain Monte Carlo (MCMC), to solve a wide range of problems. Probabilistic computations, often considered too slow on conventional processors, can be…
In this paper we study the bicausal optimal transport problem for Markov chains, an optimal transport formulation suitable for stochastic processes which takes into consideration the accumulation of information as time evolves. Our analysis…
Efficiency is a core concept of multi-objective optimization problems and multi-attribute decision making. In the case of pairwise comparison matrices a weight vector is called efficient if the approximations of the elements of the pairwise…
We introduce a novel kind of robustness in linear programming. A solution x* is called robust optimal if for all realizations of objective functions coefficients and constraint matrix entries from given interval domains there are…
Markov automata combine non-determinism, probabilistic branching, and exponentially distributed delays. This compositional variant of continuous-time Markov decision processes is used in reliability engineering, performance evaluation and…
The problem of constructing optimal AIFV codes is a special case of that of constructing minimum cost Markov Chains. This paper provides the first complete proof of correctness for the previously known iterative algorithm for constructing…
Influence diagrams represent decision-making problems with interdependencies between random events, decisions, and consequences. Traditionally, they have been solved using algorithms that determine the expected utility-maximizing decision…
A cost Markov chain is a Markov chain whose transitions are labelled with non-negative integer costs. A fundamental problem on this model, with applications in the verification of stochastic systems, is to compute information about the…
We study a general class of convex submodular optimization problems with indicator variables. Many applications such as the problem of inferring Markov random fields (MRFs) with a sparsity or robustness prior can be naturally modeled in…
We present a general framework for accelerating a large class of widely used Markov chain Monte Carlo (MCMC) algorithms. Our approach exploits fast, iterative approximations to the target density to speculatively evaluate many potential…
This paper analyzes the factorizability and geometry of transition matrices of multivariate Markov chains. Specifically, we demonstrate that the induced chains on factors of a product space can be regarded as information projections with…
This paper considers an optimal impulse control problem of dynamical systems generated by a flow. The performance criteria are total costs over the infinite time horizon. Apart from the main performance to be minimized, there are multiple…