Concentration and deviation inequalities in infinite dimensions via covariance representations

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Stochastic analysis of Bernoulli processes (2008, methodology): “[10, 16, 23], and to option pricing and hedging in discrete time mathematical finance.”
Stochastic analysis for Poisson processes (2014, background): “1 the following result was proved in [4].”
Poisson process Fock space representation, chaos expansion and covariance inequalities (2009, background): “For normal martingales the result is stated in [14].”
Density Formula and Concentration Inequalities with Malliavin Calculus (2009, background): “In [6], Houdré and Privault prove concentration inequalities for functionals of Wiener and Poisson spaces: they have discovered almost-sure conditions on expressions involving Malliavin derivatives which guarantee upper bounds on the tails of their functionals.”
Risk bounds for the non-parametric estimation of Lévy processes (2006, unknown): “3), see [25] (Proposition 7) or [18] (Corollary 5.”
Adaptive estimation of the intensity of inhomogeneous Poisson processes via concentration inequalities (2003, background): “This inequality is known and holds for more general functionals than the integrals (see [22], Corollary 5.”
Stochastic Analysis in Discrete and Continuous Settings: With Normal Martingales (2009, methodology): “This chapter is a revision of [117] with some additions, and is mainly based on [61] and [119].”