Journal article
Signature cumulants, ordered partitions, and independence of stochastic processes
- Abstract:
- The sequence of so-called signature moments describes the laws of many stochastic processes in analogy with how the sequence of moments describes the laws of vector-valued random variables. However, even for vector-valued random variables, the sequence of cumulants is much better suited for many tasks than the sequence of moments. This motivates us to study so-called signature cumulants. To do so, we develop an elementary combinatorial approach and show that in the same way that cumulants relate to the lattice of partitions, signature cumulants relate to the lattice of so-called "ordered partitions". We use this to give a new characterisation of independence of multivariate stochastic processes; finally we construct a family of unbiased minimum-variance estimators of signature cumulants.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
Actions
Access Document
- Files:
-
-
(Accepted manuscript, 493.8KB, Terms of use)
-
- Publisher copy:
- 10.3150/20-BEJ1205
Authors
- Publisher:
- Bernoulli Society for Mathematical Statistics and Probability
- Journal:
- Bernoulli More from this journal
- Volume:
- 26
- Issue:
- 4
- Pages:
- 2727-2757
- Publication date:
- 2020-08-27
- Acceptance date:
- 2020-02-10
- DOI:
- EISSN:
-
1573-9759
- ISSN:
-
1350-7265
Terms of use
- Copyright holder:
- ISI / BS
- Copyright date:
- 2020
- Rights statement:
- © ISI / BS 2020
- Notes:
- This is the accepted manuscript version of the article. The final version is available from Project Euclid at: https://doi.org/10.3150/20-BEJ1205
If you are the owner of this record, you can report an update to it here: Report update to this record