201 citations · 2.4k across the 113 of their papers we have counts for
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Levy Processes and Quasi-Shuffle Algebras
Charles Curry, Kurusch Ebrahimi-Fard, Simon J. A. Malham +1
We investigate the algebra of repeated integrals of semimartingales. We prove that a minimal family of semimartingales generates a quasi-shuffle algebra. In essence, to fulfill the…
Unfolding the double shuffle structure of q-multiple zeta values
Jaime Castillo Medina, Kurusch Ebrahimi-Fard, Dominique Manchon
We exhibit the double q-shuffle structure for the qMZVs recently introduced by Y. Ohno, J. Okuda and W. Zudilin.
On Euler's decomposition formula for qMZVs
Jaime Castillo Medina, Kurusch Ebrahimi-Fard, Dominique Manchon
In this short and elementary note we derive a q-generalization of Euler's decomposition formula for the qMZVs recently introduced by Y. Ohno, J. Okuda, and W. Zudilin. This answers…
The tridendriform structure of a Magnus expansion
Kurusch Ebrahimi-Fard, Dominique Manchon
The notion of trees plays an important role in Butcher's B-series. More recently, a refined understanding of algebraic and combinatorial structures underlying the Magnus expansion…
The pre-Lie structure of the time-ordered exponential
Kurusch Ebrahimi-Fard, Frederic Patras
The usual time-ordering operation and the corresponding time-ordered exponential play a fundamental role in physics and applied mathematics. In this work we study a new approach to…
Rota-Baxter Algebra. The Combinatorial Structure of Integral Calculus
Kurusch Ebrahimi-Fard, Frederic Patras
Gian-Carlo Rota suggested in one of his last articles the problem of developing a theory around the notion of integration algebras, complementary to the already existing theory of…