Blar i NTNU Open på forfatter "Patras, Frederic"
-
Cumulants, free cumulants and half-shuffles
Ebrahimi-Fard, Kurusch; Patras, Frederic (Peer reviewed; Journal article, 2015)Free cumulants were introduced as the proper analogue of classical cumulants in the theory of free probability. There is a mix of similarities and differences, when one considers the two families of cumulants. Whereas the ... -
Hopf-algebraic Deformations of Products and Wick Polynomials
Ebrahimi-Fard, Kurusch; Patras, Frederic; Tapia, Nikolas; Zambotti, Lorenzo (Journal article; Peer reviewed, 2018)We present an approach to cumulant–moment relations and Wick polynomials based on extensive use of convolution products of linear functionals on a coalgebra. This allows, in particular, to understand the construction of ... -
Monotone, free, and boolean cumulants: a shuffle algebra approach
Ebrahimi-Fard, Kurusch; Patras, Frederic (Journal article; Peer reviewed, 2018)The theory of cumulants is revisited in the “Rota way”, that is, by following a combinatorial Hopf algebra approach. Monotone, free, and boolean cumulants are considered as infinitesimal characters over a particular ... -
On non-commutative stochastic exponentials
Curry, Charles Henry Alexander; Ebrahimi-Fard, Kurusch; Patras, Frederic (Journal article; Peer reviewed, 2019)Using non-commutative shuffle algebra, we outline how the Magnus expansion allows to define explicit stochastic exponentials for matrix-valued continuous semimartingales and Stratonovich integrals. -
Shuffle group laws: applications in free probability
Ebrahimi-Fard, Kurusch; Patras, Frederic (Peer reviewed; Journal article, 2019)Commutative shuffle products are known to be intimately related to universal formulas for products, exponentials and logarithms in group theory as well as in the theory of free Lie algebras, such as, for instance, the ...