461 citations · 486 across the 5 of their papers we have counts for
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Decompositions of stochastic processes based on irreductible group representations
Giovanni Peccati, Jean-Renaud Pycke
Let G be a topological compact group acting on some space Y. We study a decomposition of Y-indexed stochastic processes, based on the orthogonality relations between the characters…
Anticipating integrals and martingales on the Poisson space
Giovanni Peccati, Ciprian A. Tudor
Let be a standard compensated Poisson process on . We prove a new characterization of anticipating integrals of the Skorohod type with respect to $\tilde{N}…
Central limit theorems for sequences of multiple stochastic integrals
David Nualart, Giovanni Peccati
We characterize the convergence in distribution to a standard normal law for a sequence of multiple stochastic integrals of a fixed order with variance converging to 1. Some applic…
Identities in law between quadratic functionals of bivariate Gaussian processes, through Fubini theorems and symmetric projections
Giovanni Peccati, Marc Yor
We present three new identities in law for quadratic functionals of conditioned bivariate Gaussian processes. In particular, our results provide a two-parameter generalization of a…
Hoeffding-ANOVA decompositions for symmetric statistics of exchangeable observations
Giovanni Peccati
Consider a (possibly infinite) exchangeable sequence X={X_n:1\leqn<N}, where N\in N\cup {\infty}, with values in a Borel space (A,A), and note X_n=(X_1,...,X_n). We say that X is H…