arXiv subjects

Marco Sangalli

Publications and source records attributed to Marco Sangalli.

5 recordsLinked to original sources

arXiv2026

Lower and Upper Expected Hitting Times for Weighted Imprecise Markov Chains

In this paper, we extend hitting times for imprecise Markov chains to the framework of weighted imprecise Markov chains (WIMCs), in which each transition is associated with a strictly positive weight encoded by a matrix $W$. Given a convex set $\mathcal{T}$ of admissible transition matrices, we define lower and upper expected hitting times for WIMCs as the infimum and supremum of the (weighted) expected hitting times over $\mathcal{T}$, and we characterise these quantities as the unique solutions of nonlinear fixed-point equations. We show that any weighted hitting time problem can be transformed into an unweighted hitting time problem on an augmented state space, enabling the reuse of existing IMC theory and algorithms. In particular, we are able to adapt known iterative methods for the numerical computation of expected hitting times for WIMCs.

math.PR↗

arXiv2026

Relation between Hitting Times and Probabilities for Imprecise Markov Chains

In the present paper, we investigate the relationship between hitting times and hitting probabilities in discrete-time imprecise Markov chains (IMCs). We define lower and upper hitting times and probabilities for IMCs whose set of transition matrices $\T$ is compact, convex, and has separately specified rows. Building on reachability-based partitions of the state space, we prove two key implications: (i) finiteness of the upper expected hitting time entails the lower hitting probability equals one, and (ii) finiteness of the lower expected hitting time entails the upper hitting probability equals one. We further show an equivalence: the upper expected hitting time is finite if and only if the lower hitting probability is one. Finally, by presenting a counterexample, we show that the converse of the second implication can fail.

math.PR↗

arXiv2025

Computing Lower and Upper Hitting Probabilities for Imprecise Markov Chains

We study the computation of lower and upper probabilities of hitting a target set of states for imprecise Markov chains, where transition uncertainty is modelled by a convex set of transition matrices. In the precise case, hitting probabilities are the minimal nonnegative solution of a linear system and admit a closed-form expression. We investigate the notion of reachability in the imprecise setting. The literature review highlights several different definitions of lower reachability; thus, we explore the relations among them and present examples to clarify their logical implications. Using this revised definition of reachability for imprecise Markov chains, we partition the state space into classes of states whose hitting probabilities are trivially zero or one, and those which require further computation. For these nontrivial states, we show that the lower hitting probability is the unique solution of a nonlinear fixed-point equation, while the same does not hold for upper hitting probabilities. For the practical computation of lower and upper hitting probabilities, we propose iterative algorithms that alternate between solving a linear system and choosing an extreme point from the set of transition matrices. Numerical experiments demonstrate that, in practice, these algorithms converge in substantially fewer iterations than the theoretically established worst-case bound.

math.PR↗

arXiv2025

Upper Expected Meeting Times for Interdependent Stochastic Agents

We analyse the problem of meeting times for interdependent stochastic agents: random walkers whose behaviour is stochastic but controlled by their selections from some set of allowed actions, and the inference problem of when these agents will be in the same state for the first time. We consider the case where we are epistemically uncertain about the selected actions of these agents, and show how their behaviour can be modelled using imprecise Markov chains. This allows us to use results and algorithms from the literature, to exactly compute bounds on their meeting time, which are tight with respect to our epistemic uncertainty models. We focus on the two-agent case, but discuss how it can be naturally extended to an arbitrary number of agents, and how the corresponding combinatorial explosion can be partly mitigated by exploiting symmetries inherent in the problem.

math.PR↗

arXiv2025

Towards conservative inference in credal networks using belief functions: the case of credal chains

This paper explores belief inference in credal networks using Dempster-Shafer theory. By building on previous work, we propose a novel framework for propagating uncertainty through a subclass of credal networks, namely chains. The proposed approach efficiently yields conservative intervals through belief and plausibility functions, combining computational speed with robust uncertainty representation. Key contributions include formalizing belief-based inference methods and comparing belief-based inference against classical sensitivity analysis. Numerical results highlight the advantages and limitations of applying belief inference within this framework, providing insights into its practical utility for chains and for credal networks in general.

cs.AI↗