Mathematics Colloquia and Seminars

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I will discuss an explicit construction of approximate Green's functions of certain Fokker-Planck equations in terms of Dyson series, Taylor expansions, and exact commutator formulas. Our method gives an approximate solution that is accurate to arbitrary order in time in the short-time limit, and it can be extended to large time by bootstrapping. I will also present some numerical results showing that our algorithm works well also for degenerate equations such as those arising in pricing of contingent claims.