Probability measures on metric spaces

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Representations of the Infinite Symmetric Group (2016, methodology): “The category B About the notions used in this subsection see Parthasarathy [100] and Meyer [74].”
Heavy-traffic limits for waiting times in many-server queues with abandonment (2008, background): “e triangular array (Xi,n) satisﬁes Lyapunov’s condition. Therefore, the functional Lindeberg–Feller central limit theorem applies to the partial sum sequence and we get our result; see Theorem 4.1 of [10]. We now give our main result of the section. Note that one could erroneously conclude from Theo”
Two-stage sampled learning theory on distributions (2014, unknown): “4 in [40] (page 55).”
Hybrid Monte Carlo on Hilbert spaces (2011, unknown): “The two probability measures in (42) are equal if and only if (see e.g. [21]) for any continuous bounded g .”
Stochastic Reaction-diffusion Equations Driven by Jump Processes (2010, unknown): “2 of [55], the laws of the family {ηn, n ∈ N} are tight on MN(Z × R+).”
On the Bernstein-von Mises phenomenon in the Gaussian white noise model (2011, unknown): “, [10].”
Stein’s method, Palm theory and Poisson process approximation (2004, background): “…page 95], so there exists a sequence of bounded uniformly continuous functions (fj; j ≥ 1) on H which form a determining class [Billingsley (1968), page 15]: for every two probability measures Q1 and Q2 on H, if ∫ fj dQ1 = ∫ fj dQ2 for all j ≥ 1, then Q1 =Q2 [see Parthasarathy (1967), Theorem 6.6].”
A bootstrap-assisted spectral test of white noise under unknown dependence (2011, background): “Note that L2[0, π] is endowed with the natural Borel σ -field induced by the norm ‖f ‖ = ⟨f , f ⟩1/2; see Parthasarathy (1967).”
Strictly stable distributions on convex cones (2005, background): “5) can be taken over all continuous characters on K, see [36].”
Invariant measures for Burgers equation with stochastic forcing (2000, methodology): “ τ: θτω(t) = ω(t+τ), and by Sτ ωwthe solution of (1.1) at time t= τwhen the realization of the force is ωand the initial datum at time t= 0 is w. We will denote by Dthe Skorohod space on S1 (see [B], [Pa]) consisting of functions INVARIANT MEASURES FOR BURGERS EQUATION 879 having only discontinuitie”
Mixtures of Dirichlet Processes with Applications to Bayesian Nonparametric Problems (1974, background): “If (e, JV) and (U, XW) are standard Borel spaces, then the product space (3 x U, _v x ') is a standard Borel space, and the required conditional distributions specified above are known to exist (see, for example, Parthasarathy [13] Chapter 5).”
γ-Radonifying Operators: A Survey (2010, unknown): “Excellent accounts of this result and its ramifications can be found in Billingsley [7] and Parathasarathy [95].”
Metrics for labelled Markov processes (2004, background): “An excellent mathematical resource is “Probability Measures on Metric Spaces” by K. R. Parthasarathy [ Par67 ] which deals with the dual topic i.e.”
A _{}[0,1] representation of random upper semicontinuous functions (2002, background): “Since the space (D ↑ K(B), dS) is complete and separable, (D ↑ K(B), dp) is separable, and Adp ⊂ AdS implies that the identity mapping from (D↑ K(B), dS) to (D↑ K(B), dp) is measurable, then on the basis of Kuratowski Theorem (see [20]) we conclude that AdS ⊂ Adp .”
Fluid limits of many-server queues with reneging (2010, methodology): “Then D H[0, T ] and D H[0,∞) are also Polish spaces (see [20]).”
Graphons, cut norm and distance, couplings and rearrangements (2010, background): “Some general references (from different points of view) are [6, 19, 42, 54].”