Tolerance Enforced Simulation for Stochastic Differential Equations via Rough Path Analysis
Seminar Room 1, Newton Institute
AbstractConsider a stochastic differential equation (SDE) driven by Brownian Motion which possesses a strong solution in the interval [0,t]. Given any tolerance error, say epsilon, defined in advance, we explain how to simulate a piece-wise linear path which approximates the underlying SDE in uniform norm in [0,t] with an error less than epsilon with probability one. The technique, as we shall explain, takes advantage of continuity estimates, studied in the theory of rough paths, of the Ito-Lyons map defining the underlying the SDE. (This presentation is based on joint work with Xinyun Chen and Jing Dong.)
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