An Introduction to Probability Theory and Its Applications

By W. Feller. 1959

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Citations in the corpus

A Kernel Method for the Two-Sample-Problem (2006, methodology): “For r = 1 the distance Dr(p, q) is known as the Levy distance (Feller, 1971), and for r = 2 we encounter distance measures derived from the Renyi entropy (Gokcay and Principe, 2002).”
Empirical margin distributions and bounding the generalization error of combined classifiers (2002, methodology): “Utilizing the following estimates in Stirling’s formula for the factorial (see Feller (1950)) it is straightforward to check that for some constant c > 0 (cid:0) The last inequality is due to the fact that Since γ k ≤ 1 / 2 for k ∈ K , we can continue and come to the following lower bound then for…”
Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions (2009, neutral): “This is a coupon collection problem [56].”
Mobility increases the capacity of ad-hoc wireless networks (2001, background): “2There is no closed form for the distribution or density function of I for general ; only the Laplace transform of its density is known explicitly [3], [9] and is given by (s) = exp( s ).”
Airy Distribution Function: From the Area Under a Brownian Excursion to the Maximal Height of Fluctuating Interfaces (2004, background): “Note that the location 0 ≤ t′ ≤ L of the maximum of a free Brownian motion over the interval [0, L] is a random variable whose normalized probability distribution P (t′) is well known [32], P (t′) = 1 π √ t′(L− t′) , (70) which also describes, in the context of the interface with free boundary condi”
Multiscaling fractional advection‐dispersion equations and their solutions (2003, unknown): “…simplifies to ~̂P k; sð Þ ¼ 1 llþs s 1 1 ~fo kð Þ llþs ¼ 1 s l ~fo kð Þ 1 : Inverse Laplace transform yields the Fourier transform of the compound Poisson process [Feller, 1968]: P̂ k; tð Þ ¼ exp lt ~fo kð Þ 1 ; ð6Þ where l and fo retain their meaning as jump rate parameter and jump size…”