Lectures on probability theory and statistics

By Boris Tsirelson, Wendelin Werner, Jean Picard. 2004

141 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/887b85bde5f9b8c7e30f588c13a7f2b93d17c134

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In Mathematical Physics

In Statistical and Nonlinear Physics

In Statistics and Probability

Citations in the corpus

MINIMAX ESTIMATION OF A FUNCTIONAL ON A STRUCTURED (2016, background): “Functions x 7→ χp(x) with this property are known as influence functions in semiparametric theory [13, 19, 31, 5, 2], go back to the von Mises calculus due to [29], and play an important role in robust statistics [11, 9], or [36], Chapter 20.”
Vast Portfolio Selection with Gross-exposure Constraints (2012, unknown): “The proof follows similar arguments on page 188 of Emery, Nemirovski, and Voiculescu (2000) and Dumbgen et al. (2010).”
Localization and delocalization of random interfaces (2005, background): “The dynamical aspects of these models are of great interest and are also discussed in [55].”
Statistical performance of support vector machines (2008, background): “4) (with the square loss `(x, y) = (x− y)2 replacing the hinge loss) is completely elucidated (see [25], Section 4.”
Energy inequalities for cutoff functions and some applications (2012, background): “More general possibilities can arise; for various exact fractals (see [Ba1]) one can have V (x, r) ≍ r and a space time scaling of t = r, where α ∈ [1,∞) and β ∈ [2, 1 + α]; the case when β 6= 2 is called anomalous diffusion.”
Propagating Lyapunov functions to prove noise-induced stabilization (2011, methodology): “Translating [3] to our current setting, we obtain the following theorem: Theorem 11.”
Time-changed CIR default intensities with two-sided mean-reverting jumps (2014, unknown): “…kernel, φ(λ) is a Lévy exponent, γ ≥ 0 is the nonnegative drift and ν(ds) is a Lévy measure of the subordinator that satisfies the integrability condition ∫ (0,∞)(s ∧ 1)ν(ds) ∞ [standard references on subordinators are Bertoin (1996, 1999), Sato (1999) and Schilling, Song and Vondraček (2010)].”
Stability of heat kernel estimates for symmetric non-local Dirichlet forms (2016, methodology): “This is the case, for example, for the Sierpinski gasket in R (n ≥ 2) which is a d-set with d = log(n+ 1)/ log 2 and has walk dimension dw = log(n+ 3)/ log 2, and for the Sierpinski carpet in R (n ≥ 2) which is a d-set with d = log(3 − 1)/ log 3 and has walk dimension dw > 2; see [B].”