(1) Malliavin calculus has been used in mathematical finance to compute sensitivity parameters of option prices, see these lecture notes and this research article.

(2) Hida's white-noise infinite dimensional calculus relies on built-in spaces of stochastic distributions (Hida and Kondratiev spaces). The Malliavin calculus is more flexible, in that it allows one to build solution spaces optimal for the equation at hand. In A Stochastic Modeling Methodology Based on Weighted Wiener Chaos and Malliavin Calculus this feature of Malliavin calculus was used to obtain more powerful numerical approximation schemes than would follow from Hida distributions.

(1) Malliavin calculus has been used in mathematical finance to compute sensitivity parameters of option prices, see these lecture notes and this research article. And Statistical inference and Malliavin calculus is a more general application of Malliavin calculus to statistics.

(2) Hida's white-noise infinite dimensional calculus relies on built-in spaces of stochastic distributions (Hida and Kondratiev spaces). The Malliavin calculus is more flexible, in that it allows one to build solution spaces optimal for the equation at hand. In A Stochastic Modeling Methodology Based on Weighted Wiener Chaos and Malliavin Calculus this feature of Malliavin calculus was used to obtain more powerful numerical approximation schemes than would follow from Hida distributions.