Non-abelian ZZ-theory: Berends-Giele recursion for the α′\alpha'-expansion of disk integrals

We present a recursive method to calculate the $\alpha'$-expansion of disk integrals arising in tree-level scattering of open strings which resembles the approach of Berends and Giele to gluon amplitudes. Following an earlier interpretation of disk integrals as doubly partial amplitudes of an effective theory of scalars dubbed as $Z$-theory, we pinpoint the equation of motion of $Z$-theory from the Berends-Giele recursion for its tree amplitudes. A computer implementation of this method including explicit results for the recursion up to order $\alpha'^7$ is made available on the website http://repo.or.cz/BGap.gitComment: 58 pages, harvmac TeX, v2: cosmetic changes, published versio

Algebraic Structures and Stochastic Differential Equations driven by Levy processes

We construct an efficient integrator for stochastic differential systems driven by Levy processes. An efficient integrator is a strong approximation that is more accurate than the corresponding stochastic Taylor approximation, to all orders and independent of the governing vector fields. This holds provided the driving processes possess moments of all orders and the vector fields are sufficiently smooth. Moreover the efficient integrator in question is optimal within a broad class of perturbations for half-integer global root mean-square orders of convergence. We obtain these results using the quasi-shuffle algebra of multiple iterated integrals of independent Levy processes.Comment: 41 pages, 11 figure