Malliavin calculus and tightness of probability measures

The purpose of this talk is to discuss the applications of the stochastic calculus of variations or Malliavin calculus to proving  tightness in the context of functional central limit theorems.  The moment estimates that imply the required tightness property  are obtained using Meyer’s inequalities and a suitable representation of centered random variables as the divergence of a random field. We will apply this approach to the asymptotic behavior of the renormalized self-intersection local time of a d-dimensional fractional Brownian motion and to the Breuer-Major theorem for functionals of a stationary Gaussian process.