Semicircular limits on the free Poisson chaos: Counterexamples to a transfer principle

We establish a class of sufficient conditions ensuring that a sequence of multiple integrals with respect to a free Poisson measure converges to a semicircular limit. We use this result to construct a set of explicit counterexamples showing that the transfer principle between classical and free Brownian motions (recently proved by Kemp, Nourdin, Peccati and Speicher (2012)) does not extend to the framework of Poisson measures. Our counterexamples implicitly use kernels appearing in the classical theory of random geometric graphs. Several new results of independent interest are obtained as necessary steps in our analysis, in particular: (i) a multiplication formula for free Poisson multiple integrals, (ii) diagram formulae and spectral bounds for these objects, and (iii) a counterexample to the general universality of the Gaussian Wiener chaos in a classical setting.     

Asymptotic Theory for Fractional Regression Models via Malliavin Calculus

We study the asymptotic behavior as n→∞ of the sequence

Density Estimates for Solutions to One Dimensional Backward SDE’s

In this paper, we derive sufficient conditions for each component of the solution to a general backward stochastic differential equation to have a density for which upper and lower Gaussian estimates can be obtained.     

Berry-Esséen Bounds for Long Memory Moving Averages via Stein's Method and Malliavin Calculus

Using the Stein method on Wiener chaos introduced in Nourdin and Peccati [10], we prove Berry-Esséen bounds for long memory moving averages.