Flows associated to adapted vector fields on the Wiener space

The existence and uniqueness of a flow associated to an adapted vector field ξ on the Wiener space with dτ ξα = a β α dωβ(τ ) + bα dτ are proved by a modified Picard’s iteration method, mainly under the conditions of exponential integrability concerning bα as well as the first-order Malliavin gradients of a β α and bα. A Newton–Leibnitz type inequality for a kind of Malliavin differentiable functionals is also proved, which is the key point to prove the above result, and has an independent interest. © 2007 Elsevier Inc. All rights reserved