A multiple coupon collection process and its Markov embedding structure
Abstract
Abstract The embedding problem of Markov transition matrices into continuous-time Markov semigroups is a classic problem that regained a lot of impetus and activities in recent years. We consider it here for the following generalisation of the well-known coupon collection process: from a finite set of distinct objects, a subset is drawn repeatedly according to some probability distribution, independently and with replacement, and each time united with the set of objects sampled so far. We derive and interpret properties of and explicit conditions for the resulting discrete-time Markov chain to be representable within a semigroup or a flow of a continuous-time process of the same type.
Fields of Study & Subjects
Stochastic processes and statistical mechanics
Publication details
- Journal / source
- Monatshefte für Mathematik
- Publisher
- Springer Science and Business Media LLC
- Volume
- 209
- Issue
- 3
- Pages
- 357–381
- Publication date
- 30 January 2026
- Language
- EN