An extension of lévy's stochastic area formula

Abstract

We obtain an extension of Levy's formula in which the two dimensional Brownian motion in addition to being conditioned by its value at time t = 1 as in the classical formula, is also conditioned by the values of the integral of each of its components with respect to some given measures on the time interval (0,1).

Keywords:

• Brownian motion
• Levy's stochastic area formula
• abstract Wiener space
• Fourier-Wiener transform