An Introduction to Probability Theory and its Applications, Volume I

By B. Harshbarger. 1958

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Citations in the corpus

Private Counting from Anonymous Messages: Near-Optimal Accuracy with Vanishing Communication Overhead (2020, background): “To prove Lemma 15, we will resort to Feller’s characterization (Feller, 1968) of infinitely divisible distribution as a discrete compound Poisson distribution.”
Limit theorems for empirical Fr\'echet means of independent and non-identically distributed manifold-valued random variables (2011, background): “The reader will see that the arguments in this section are almost entirely classical [see, e.g., Feller (1966)] and the main issue is simply to formulate the result.”
Confidence bands for Brownian motion and applications to Monte Carlo simulation (2007, background): “a Brownian motion Let (Wt)t∈[0,1] be a standard Brownian motion (Feller, 1971).”
Sampling nested Archimedean copulas (2008, background): “The derivative is h′(t) = f ′(g(t))g′(t) on t > 0 and two lemmas of Feller [6] (see also Nelsen [2, p.”
A tutorial introduction to the minimum description length principle (2004, background): “By the law of large numbers [Feller 1968], we immediately see that the ‘sum of mistake probabilities’ ∑ j P (θ̂(x n) 6= θj|θj) tends to 0 as n grows.”
A new approach to channel access scheduling for Ad Hoc networks (2001, background): “This situation has been formulated as an occupancy problem in combinatorial mathematics [10] [18], which pursues the probability of having m empty cells after randomly placing r balls into n cells, where r corresponds to the block size, and n corresponds to the number of two-hop neighbors of a new m”
Capacity, delay and mobility in wireless ad-hoc networks (2003, methodology): “+ Im, we use the limit theorem for sums of Pareto distribution with exponent less than 1 [1].”
Random Graphs and Complex Networks (2016, background): “We again refer to [36], or to introductory books in probability, such as [37, 89, 90, 94].”
Comparative Analyses of Expected Shortfall and Value-at-Risk: Their Estimation Error, Decomposition, and Optimization (2002, background): “4 For details of the stable distribution, see Feller [1969] and Shiryaev [1999].”
An elementary introduction to the Wiener process and stochastic integrals (2010, background): “Lemma 1 For each m ≥ 0, S̃m(t) (t ≥ 0) is a random walk, that is, X̃m(1), X̃m(2), .”