Distances of Probability Measures and Random Variables

By R. Dudley. 1968

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Citations in the corpus

Gossip Dual Averaging for Decentralized Optimization of Pairwise Functions (2016, methodology): “ = (1=p k) P t s=1 k(t). Since ( k(t)) t1 is a Bernoulli process of parameter 1=p k, by the law of Gossip Dual Averaging for Decentralized Optimization of Pairwise Functions iterative logarithms (Dudley, 2010), (Nedic, 2011, Lemma 3) one has with probability 1 and for any´ q>0 lim t!+1 jm k(t) t”
On Choosing and Bounding Probability Metrics (2002, background): “This was shown by Strassen (1965) for complete separable metric spaces and extended by Dudley (1968) to arbitrary separable metric spaces.”
Testing hypotheses in the functional linear model (2003, background): “Let us note by the Prohorov metric which induces the topology of weak convergence on the set of S-valued random variables where S is some separable metric space (see Dudley, 1968).”
Ambiguous chance constrained problems and robust optimization (2006, background): “extended to arbitrary separable metric spaces by Dudley [ 15 ].”
Convergence of algorithms for reconstructing convex bodies and directional measures (2006, unknown): “µ,ν). (88) Let 0 < ε < d P(m 0µ 1,m 0ν 1). By (79), there is a closed set F in Sn−1 such that µ 1(F)>ν 1(Fε)+ ε m 0 or ν 1(F)>µ 1(Fε)+ ε m 0 . Setting α=ε/m 0 and β =ε in Proposition 3 of [6], we obtain 2 m 0(2+ε) (89) ε2 ≤d D(µ 1,ν 1). By (79) again, we have d P(µ 1,ν 1)≤1 and d P(m 0µ ”
COMPLEX UNIT ROOTS AND BUSINESS CYCLES: ARE THEY REAL? (2000, background): “In analyzing the asymptotic properties of continuous functions of W1;n and/or W2;n, it often su¢ces to analyze the properties of the same functions of the independent standard Wiener processes W1;W2;because of the Skorohod (1956), Dudley (1968) , and Wichura (1970) representation theorem.”
Limiting Behavior of Invariant Measures of Stochastic Delay Lattice Systems (2021, background): “, [20]) that Pn weakly convergent to P in P(C([−ρ, 0], l2)) if and only if dL (Pn, P) → 0.”