4 papers
The Moments of Lévy's area using a sticky shuffle Hopf algebra
Robin Hudson, Uwe Schauz, Wu Yue
Lévy's stochastic area for planar Brownian motion is the difference of two iterated integrals of second rank against its component one-dimen\-sional Brownian motions. Such iterated…
Moments of quantum Lévy areas using sticky shuffle Hopf algebras
Robin Hudson, Uwe Schauz, Yue Wu
We study a family of quantum analogs of Lévy's stochastic area for planar Brownian motion depending on a variance parameter which deform to the classical Lévy area as $σ\…
On a quantum causal stochastic double product integral related to Lévy area
Robin Hudson, Yuchen Pei
We study the family of causal double product integrals \begin{equation*} \prod_{a < x < y < b}\left(1 + i{λ\over 2}(dP_x dQ_y - dQ_x dP_y) + i {μ\over 2}(dP_x dP_y + dQ_x dQ_y)\rig…
Double product integrals and Enriquez quantisation of Lie bialgebras II: The quantum Yang-Baxter equation
R. L. Hudson, S. Pulmannova
For a Lie algebra with Lie bracket got by taking commutators in a nonunital associative algebra L, let T(L) be the vector space of tensors over L equipped with the Ito Hopf algebra…