2021
DOI: 10.1002/adts.202000274
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The Augmented Jump Chain

Abstract: Modern methods of simulating molecular systems are based on the mathematical theory of Markov operators with a focus on autonomous equilibrated systems. However, non‐autonomous physical systems or non‐autonomous simulation processes are becoming more and more important. A representation of non‐autonomous Markov jump processes is presented as autonomous Markov chains on space‐time. Augmenting the spatial information of the embedded Markov chain by the temporal information of the associated jump times, the so‐ca… Show more

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Cited by 3 publications
(3 citation statements)
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“…For our analysis, we use the fact that a (continuous-time) Markov jump process (X(t)) t≥0 has a discrete-time representation given by the augmented Markov chain [31] which assigns to each discrete index n the random time T n where the nth jump of the process occurs, as well as the state X n = X(T n ) entered by the process at this jump time. The random sequence (X n ) n∈N0 of states, called embedded Markov chain, is a standard (discrete-time) Markov chain on a countable state space.…”
Section: Resultsmentioning
confidence: 99%
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“…For our analysis, we use the fact that a (continuous-time) Markov jump process (X(t)) t≥0 has a discrete-time representation given by the augmented Markov chain [31] which assigns to each discrete index n the random time T n where the nth jump of the process occurs, as well as the state X n = X(T n ) entered by the process at this jump time. The random sequence (X n ) n∈N0 of states, called embedded Markov chain, is a standard (discrete-time) Markov chain on a countable state space.…”
Section: Resultsmentioning
confidence: 99%
“…That is, we can consider a division of the Markov jump process into the process of jump times (T n ) n∈N0 with values in [0, ∞) and the process of the states (X n ) n∈N0 in X which is called the embedded Markov chain. The discrete-time process (X n , T n ) n∈N0 is called the augmented Markov chain [31].…”
Section: The Reaction Jump Processmentioning
confidence: 99%
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