540 | RWTH Publication No: 808856 2020 |

TITLE | Low-rank tensor methods for Markov chains with applications to tumor progression models |

AUTHORS | Peter Georg, Lars Grasedyck, Maren Klever, Rudolf Schill, Rainer Spang, Tilo Wettig |

ABSTRACT | Continuous-time Markov chains describing interacting processes exhibit a state space that grows exponentially in the number of processes. This state-space explosion renders the computation or storage of the time-marginal distribution, which is defined as the solution of a certain linear system, infeasible using classical methods. We consider Markov chains whose transition rates are separable functions, which allows for an efficient low-rank tensor representation of the operator of this linear system. Typically, the right-hand side also has low-rank structure, and thus we can reduce the cost for computation and storage from exponential to linear. Previously known iterative methods also allow for low-rank approximations of the solution but are unable to guarantee that its entries sum up to one as required for a probability distribution. We derive a convergent iterative method using low-rank formats satisfying this condition. We also perform numerical experiments illustrating that the marginal distribution is well approximated with low rank. |

KEYWORDS | marginal distribution, Stochastic Automata Networks, Mutual Hazard Networks |

DOI | 10.1007/s00285-022-01846-9 |

PUBLICATION | Journal of mathematical biology 86(1), pp/article no. 7 2023 & 2022 Impressum Berlin ; Heidelberg ; New York ; Springer ISSN1432-1416 Published: 02 December 2022 |