Ito's Formula is the Chain Rule with Wick Ordering

by R. L. Hudson and R. F. Streater

Phys. Lett., 86A, pp 277-279, 1981.

ABSTRACT

We show that in the Fock space formalism of stochastic calculus, Ito's rule is essentially the ordinary chain rule, combined with Wick ordering.

A chat-room discussion of Ito's rule appears here, on Paul Wilmott's website; it is pointed out that essentially the same remark as in our paper (for the classical case) is to be found in Barry Simon's book, Functional Integration and Quantum Physics, 1979, on page 155.