Mathematical Finance and Stochastic Analysis seminar: Superdiffusive limits for deterministic fast-slow dynamical systems

Event details

I will present fast-slow systems with deterministic dynamics and random initial conditions in which the fast variable exhibits convergence to a pure jump stable Lévy process. Using p-variation methods inspired by rough path theory, we show that the slow variable converges to the solution of a Marcus differential equation but in a topology which is not any of the classical Skorokhod topologies. We describe this topology with the use of path functions which keep track of how the jumps are traversed in infinitesimal time. These results extend earlier work of Gottwald-Melbourne to the multi-dimensional setting, and we show that a range of dynamical systems fit this framework, including intermittent maps of Pomeau-Manneville type. Based on joint work with Peter Friz, Alexey Korepanov, and Ian Melbourne.

P.S. Joint with  East Midlands Stochastic Analysis Seminar sponsored by the London Mathematical Society.