Sikorski, Alexander and Weber, Marcus and Schütte, Christof
(2021)
*The augmented jump chain – a sparse representationof time-dependent Markov jump processes.*
Advanced Theory and Simulations, 4(4):2000274, 2021, 4
(4).

Full text not available from this repository.

Official URL: https://doi.org/10.1002/adts.202000274

## Abstract

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-called augmented jump chain is derived. The augmented jump chain inherits the sparseness of the infinitesimal generator of the original process and therefore provides a useful tool for studying time-dependent dynamics even in high dimensions. Furthermore, possible generalizations and applications to the computation of committor functions and coherent sets in the non-autonomous setting are discussed. After deriving the theoretical foundations, the concepts with a proof-of-concept Galerkin discretization of the transfer operator of the augmented jump chain applied to simple examples are illustrated.

Item Type: | Article |
---|---|

Subjects: | Mathematical and Computer Sciences > Mathematics > Applied Mathematics |

Divisions: | Department of Mathematics and Computer Science > Institute of Mathematics |

ID Code: | 2718 |

Deposited By: | Monika Drueck |

Deposited On: | 11 Feb 2022 14:35 |

Last Modified: | 18 Mar 2022 14:30 |

Repository Staff Only: item control page