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