An Introduction to Infinite-Dimensional Analysis

By Giuseppe Da Prato. 2006

414 citations recorded by the source corpus.

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In Mechanics of Materials

Citations in the corpus

7 – Backward Stochastic Differential Equations (2011, neutral): “W(1,2) is the Sobolev space of random variables defined as in Da Prato [23].”
On Bayesian A- and D-optimal experimental designs in infinite dimensions (2014, background): “, Reed and Simon (1972), Da Prato and Zabczyk (2002, Chapter 1), or Gel’fand and Vilenkin (1964). Moreover, it is straightforward to show that if A is a trace-class operator and B : H → R is a bounded linear operator, then AB∗B ∈ L1(H ) and tr(AB∗B) = tr(BAB∗).”
Introduction to stochastic partial differential equations (2008, background): “If T ∈ L(U,H)0, then, by property (3) in Remark 1.”
A Logical Theory of Localization (2015, background): “(It remains to be seen whether probability theory on high dimensions [10,15] can be adapted for the purposes of a model of belief.”
Bayesian inverse problems with non-conjugate priors (2012, neutral): “7 of [8]) shows that for any f ∈ H1, this measure is equivalent to ⊗∞ k=1N(0, n −1) with affinity exp(−n8 ∑ k ρ 2 kf 2 k ) > 0.”
Tighter PAC-Bayes bounds through distribution-dependent priors (2013, background): “See, for example ([13], Chapter 1) for a discussion of such Gaussian probability measures on an infinite dimensional Hilbert space.”
Asymptotic Behavior of Stochastic Wave Equations with Critical Exponents on R^3 (2008, background): “The reader is referred to [15] for more details on the theory of Wiener processes.”
The Bayesian Approach to Inverse Problems (2013, background): “For further reading on Gaussian measures, see [27].”
Sparse tensor discretizations of high-dimensional parametric and stochastic PDEs* (2011, methodology): “, Holden, Oksendal, Uboe and Zhang (1996), Da Prato and Zabczyk (1992), Da Prato (2006), Lototsky and Rozovskii (2006), Prévôt and Röckner (2007), Dalang, Khoshnevisan, Mueller, Nualart and Xiao (2009) and the references therein), PDEs with random inputs in numerical simulation in science and engine”
Asymptotic behavior of stochastic wave equations with critical exponents on $\mathbb{R}^{3}$ (2008, background): “The reader is referred to [15] for more details on the theory of Wiener processes.”