The Lie Bracket of Adapted Vector Fields on Wiener Spaces

  title={The Lie Bracket of Adapted Vector Fields on Wiener Spaces},
  author={B. K. Driver},
  • B. K. Driver
  • Published 1998
LetW(M)be the based (at o ∈ M)path space of a compact Riemannian manifoldM equipped with Wiener measure ν. This paper is devoted to considering vector fields onW(M) of the form Xh s (σ ) = Ps(σ )hs(σ ) where Ps(σ ) denotes stochastic parallel translation up to time s along a Wiener pathσ ∈ W(M) and {hs}s∈[0,1] is an adaptedToM-valued process on W(M). It is shown that there is a large class of processes h (called adapted vector fields) for which we may view Xh as first-order differential… CONTINUE READING

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