Geodesic
Unified signature cumulants and generalized Magnus expansions
Forum of Mathematics, Sigma, Tome 10 (2022)

Voir la notice de l'article provenant de la source Cambridge University Press

The signature of a path can be described as its full non-commutative exponential. Following T. Lyons, we regard its expectation, the expected signature, as a path space analogue of the classical moment generating function. The logarithm thereof, taken in the tensor algebra, defines the signature cumulant. We establish a universal functional relation in a general semimartingale context. Our work exhibits the importance of Magnus expansions in the algorithmic problem of computing expected signature cumulants and further offers a far-reaching generalization of recent results on characteristic exponents dubbed diamond and cumulant expansions with motivations ranging from financial mathematics to statistical physics. From an affine semimartingale perspective, the functional relation may be interpreted as a type of generalized Riccati equation. 
@article{10_1017_fms_2022_20,
     author = {Peter K. Friz and Paul P. Hager and Nikolas Tapia},
     title = {Unified signature cumulants and generalized {Magnus} expansions},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
     volume = {10},
     year = {2022},
     doi = {10.1017/fms.2022.20},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2022.20/}
}
TY  - JOUR
AU  - Peter K. Friz
AU  - Paul P. Hager
AU  - Nikolas Tapia
TI  - Unified signature cumulants and generalized Magnus expansions
JO  - Forum of Mathematics, Sigma
PY  - 2022
VL  - 10
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1017/fms.2022.20/
DO  - 10.1017/fms.2022.20
LA  - en
ID  - 10_1017_fms_2022_20
ER  - 
%0 Journal Article
%A Peter K. Friz
%A Paul P. Hager
%A Nikolas Tapia
%T Unified signature cumulants and generalized Magnus expansions
%J Forum of Mathematics, Sigma
%D 2022
%V 10
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1017/fms.2022.20/
%R 10.1017/fms.2022.20
%G en
%F 10_1017_fms_2022_20
Peter K. Friz; Paul P. Hager; Nikolas Tapia. Unified signature cumulants and generalized Magnus expansions. Forum of Mathematics, Sigma, Tome 10 (2022). doi: 10.1017/fms.2022.20

Cité par Sources :