Probability: A Graduate Course

By A. Gut. 2005

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A Stochastic Optimal Power Flow Problem With Stability Constraints—Part II: The Optimization Problem (2013, background): “The cumulants {κj}j=1 of the random variable X are defined through the cumulant generating function [17]”
OFDM Radar Algorithms in Mobile Communication Networks (2014, methodology): “An upper bound of the right-hand term can be found by applying Markov’s inequality [117], Pr [Ynd ≥ ω] ≤ 1 ω E [Ynd] .”
Moments of random multiplicative functions, II: High moments (2018, background): “If the n are Rademacher or Steinhaus random variables,3 then Khintchine’s inequality (see e.g., Lemma 3.8.1 of Gut [2013]) in fact implies that E ∣∣∑ n≤N an n ∣∣2q q (∑n≤N |an|2)q for all real q ≥ 0.”
On weighted cumulative residual entropy (2017, neutral): “Since (α1,3 + · · · + αn,3)1/3 (α1,2 + · · · + αn,2)1/2 ≈ n −1/6 → 0 as n → ∞, therefore, Lyapunov’s condition of the central limit theorem is satisfied (see Gut, 2005), which completes the proof.”
MOMENTS OF RANDOM MULTIPLICATIVE FUNCTIONS, I: LOW MOMENTS, BETTER THAN SQUAREROOT CANCELLATION, AND CRITICAL MULTIPLICATIVE CHAOS (2017, background): “The books of Gut [8] and of Montgomery and Vaughan [20] may be consulted as excellent general references for probabilistic and number theoretic background.”