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Analysis of Markov Jump Processes under Terminal Constraints

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 12651)

Abstract

Many probabilistic inference problems such as stochastic filtering or the computation of rare event probabilities require model analysis under initial and terminal constraints. We propose a solution to this bridging problem for the widely used class of population-structured Markov jump processes. The method is based on a state-space lumping scheme that aggregates states in a grid structure. The resulting approximate bridging distribution is used to iteratively refine relevant and truncate irrelevant parts of the state-space. This way, the algorithm learns a well-justified finite-state projection yielding guaranteed lower bounds for the system behavior under endpoint constraints. We demonstrate the method’s applicability to a wide range of problems such as Bayesian inference and the analysis of rare events.

Keywords

  • Bayesian Inference
  • Bridging problem
  • Smoothing
  • Lumping
  • Rare Events.

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Backenköhler, M., Bortolussi, L., Großmann, G., Wolf, V. (2021). Analysis of Markov Jump Processes under Terminal Constraints. In: Groote, J.F., Larsen, K.G. (eds) Tools and Algorithms for the Construction and Analysis of Systems. TACAS 2021. Lecture Notes in Computer Science(), vol 12651. Springer, Cham. https://doi.org/10.1007/978-3-030-72016-2_12

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  • DOI: https://doi.org/10.1007/978-3-030-72016-2_12

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