Probability Essentials

By L. Shepp. 2002

Subfields: Probabilistic & Bayesian Methods

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Citations in the corpus

Beyond CCA: Moment Matching for Multi-View Models (2016, background): “The SCF completely deﬁnes the probability distribution of x (see, e.g., Jacod & Protter, 2004).”
Consistent Nonparametric Tests of Independence (2010, methodology): “To see how this operator may be used to test independence, we recall the following characterization of independence (see, e.g., Jacod and Protter, 2000, Theorem 10.1e): While the bounded continuous functions are too rich a class to permit the construction of a covariance-based test statistic on a…”
Stochastic Analysis in Discrete and Continuous Settings: With Normal Martingales (2009, background): “1 in [71], implies that (E [F | Fn])n∈N converges to F a.”
Stochastic analysis of Bernoulli processes (2008, background): “1 in [18], implies that (E[F | Fn])n∈N converges to F a.”
The zeros of random polynomials cluster uniformly near the unit circle (2004, background): “The fact that almost sure convergence for bounded variables implies the convergence in the p th mean is a classical result in probability theory (see, for example, [11]).”
Bernstein-like Concentration and Moment Inequalities for Polynomials of Independent Random Variables: Multilinear Case (2011, background): “One sufficient condition is that the Yi are identically distributed with finite variance [9].”
Discussion of: Brownian distance covariance (2009, methodology): “To see how this operator may be used to test independence, we recall the following characterization of independence [see, e.g., Jacod and Protter (2000), Theorem 10.1e]: THEOREM 3.2.”
Global Aspects of Ergodic Group Actions (2010, background): “Some references here are Jacod-Protter [JP], §16, Glasner [Gl2], pp.”
Binary Opinion Dynamics with Stubborn Agents (2013, background): “(39) is due to the partitioning theorem [Jacod and Protter 2000].”
THE SELF-AVOIDING WALK (2006, methodology): “Although the idea of convergence in distribution has been already mentioned, we will now present the formal definitions according to Protter and Jacod [6].”
Mod-Gaussian convergence: new limit theorems in probability and number theory (2008, background): “1 in [8]) that the sequence of measures N is relatively compact for the weak convergence (or, tight).”