| Citation | Lyons' deep insight and breadth of vision have allowed him to sharpen and extend probability theory and potential theory in several fundamental ways. He has solved some tough problems in potential theory, both via the use of probability theory and, in collaboration with Hayman, directly. His profound new calculus of differential equations driven by rough (nowhere differentiable) signals gives very welcome robustness to the celebrated Ito calculus of Brownian paths, yielding clearer understanding of stochastic flows and more effective numerical techniques. More importantly, it allows stochastic calculus to be extended to much wilder processes such as Brownian motions on fractals. |