Integration with respect to local time

摘要

Let (L-t(x);x is an element ofR,t greater than or equal to0) be the local time process of a linear Brownian motion B. We integrate the Borel functions on RxR+ with respect to (L-t(x);x is an element ofR,t greater than or equal to0). This allows us to write Ito's formula for new classes of functions, and to define a local time process of B on any borelian curve. Some results are extended from deterministic to random functions. [References: 17]