On a Chen–Fliess approximation for diffusion functionals

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JournalMonatshefte fur Mathematik
DateE-pub ahead of print - 20 Aug 2014
DatePublished (current) - 2014
Issue number4
Volume175
Number of pages17
Pages (from-to)577-593
Early online date20/08/14
Original languageEnglish

Abstract

We show that the so-called functional derivatives, as recently introduced by Dupire (Functional Ito calculus, SSRN, 2010), can provide intuitive meaning to classic expansions of path dependent functionals that appear in control theory (work of Brockett, Fliess, Sussmann et. al). We then focus on stochastic differential equations and show that vector fields can be lifted to act as derivations on such functionals. This allows to revisit and generalize the classic stochastic Taylor expansion to arrive at a Chen–Fliess approximation for smooth, path dependent functionals of SDEs with a corresponding (formula presented)-error estimate.

    Research areas

  • Chen–Fliess series, Control theory, Stochastic Taylor expansion

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