An Introduction to Probability Theory and Its Applications

By David Freedman, W. Feller. 1967

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Citations in the corpus

A Kernel Method for the Two-Sample-Problem (2006, methodology): “ensity estimates (Anderson et al., 1994) is a special case of the biased MMD in equation (6). Denote by Dr(p,q) := kp−qkr the Lr distance. 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 a”
Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions (2009, background): “ kWk = 1. Suppose that we sample random rows from W to produce a matrix X. To ensure that σk(X) > 0, we must pick at least one copy each of the k distinct rows. This is a coupon collection problem [56]. It is well known that, to obtain a complete set of k coupons (i.e., rows) with nonnegligible p”
Asymptotic laws for compositions derived from transformed subordinators (2004, unknown): “for each c>0. Thus, it is suﬃcient to exploit Potter’s bound for ℓ 0 on [c,∞[. APPENDIX A.1. Abel–Tauberian theorems. An exposition of Abel–Tauberian theorems for the Laplace transform is given in [9], Section XIII.5. Bingham, Goldie and Teugels ([6], Section 1.7 and Chapter 4) give a fuller acco”
Multifractality in Asset Returns: Theory and Evidence (2002, background): “In mathematics, subordination differs from compounding, and requires that u (t) have independent increments (Bochner, 1955; Feller, 1968).”
Spectral analysis of semigroups and growth-fragmentation equations (2013, unknown): “42) (see [35, 36, 62]).”
Repeated Games with Frequent Signals (2009, methodology): “This requires us to use a “large deviations” argument that extends an argument from Feller [1972] from the sum of i.”
Uncovering individual and collective human dynamics from mobile phone records (2007, background): “main panel of the ﬁgure using ∆T a = 8.2 hours, which is the average interevent time measured for the whole population. This result, clearly diﬀerent from the one predicted by a Poisson approximation [26, 33, 34], would for instance aﬀect the predictions of spreading dynamics through the network of ”