2026/07/21 by Lorenzo Agabiti, Alberto Bonicelli, Lorenzo Zambotti
#math.PR #math.CO #math.RA
In this article we establish global a priori estimates on the solution of a generic rough differential equation driven by an α-Hölder path covering the full range of regularity α∈(0,1), under the hypothesis of Lipschitz continuity (but neither boundedness nor coercivity) of specific combinations of the coefficients and their derivatives, called elementary differentials. Our main tool is a closed formula for the remainder of a generalised Taylor expansion in terms of products of gradients of the elementary differentials, which allows to take advantage of cancellations in an optimal way.