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math.PR2025
The Arnoldi Aggregation for Approximate Transient Distributions of Markov Chains
Patrick Sonnentag, Fabian Michel, Markus Siegle
The paper proposes a new aggregation method, based on the Arnoldi iteration, for computing approximate transient distributions of Markov chains. This aggregation is not partition-b…
math.PR2025
Formal Approximations of the Transient Distributions of the M/G/1 Workload Process
Fabian Michel, Markus Siegle
This paper calculates transient distributions of a special class of Markov processes with continuous state space and in continuous time, up to an explicit error bound. We approxima…
math.PR2024
Formal Error Bounds for the State Space Reduction of Markov Chains
Fabian Michel, Markus Siegle
We study the approximation of a Markov chain on a reduced state space, for both discrete- and continuous-time Markov chains. In this context, we extend the existing theory of forma…