Stochastic Analysis in Discrete and Continuous Settings: With Normal Martingales

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Multi-Dimensional Gaussian Fluctuations on the Poisson Space (2010, background): “We also set The reader is referred e.g. to Privault [21] for a complete discussion of multiple Wiener-Itˆo integrals and their properties (including the forthcoming Proposition 2.3 and Proposition 2.4) – see also [14, 24].”
Normal approximation on Poisson spaces: Mehler’s formula, second order Poincaré inequalities and stabilization (2014, methodology): “13) which was proven for the special case of a finite Poisson process with a diffuse intensity measure in [45].”
Stochastic analysis for Poisson processes (2014, background): “12) which was proved in [27] for the special case of a finite Poisson process with a diffuse intensity measure.”
Invariance Principles for Homogeneous Sums: Universality of Gaussian Wiener Chaos (2009, background): “tic analysis. When d= 2, they are typical examples of quadratic forms. For general d, homogeneous sums are, for example, the basic building blocks of the Wiener, Poisson and Walsh chaoses (see, e.g., [24]). Despite the almost ubiquitous nature of homogeneous sums, results concerning the normal appro”
Normal Approximation of Poisson Functionals in Kolmogorov Distance (2012, background): “For more details on Malliavin calculus for Poisson functionals, we refer to [8,10,11,13] and the references therein.”