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24 Mar 2010: I. Stewart. this has resulted in algorithms, e.g. Chiu (1992), that achieve the optimal rate of convergence of therelative error, namely Op(n1/2), where n is the sample size,

30 Nov 2011: The Annals of Applied Probability2009, Vol. 19, No. 5, 1719–1780DOI: 10.1214/08-AAP591 Institute of Mathematical Statistics, 2009. STATE SPACE COLLAPSE AND DIFFUSION APPROXIMATIONFOR A NETWORK OPERATING UNDER A FAIR BANDWIDTH. SHARING POLICY. BY

14 Dec 2005: "!$#&%'() ,. -. /10 2&354 6798"79:. ;=<?>A@CBEDF<AGIHJ@K@CLJ<NMOHEPQR@TSVUXWOBEDYMZBE[[<]DMV>_LJWWVUbaOcEBdUfegRhdhdijkW_@l<AG5m_DF<_mH]DF<?npo"Pf@qLsrKPt[NPX@CDuPvGIwkHx@ly?WOBEDzHJG)H{QJn|rHx}EPn;<A}dPtQ. ]]{_{Rdd! "$#%&' )(", "-&.0/21

14 May 2016: Lecture Notes on Stochastic Networks. Frank Kelly and Elena Yudovina. Contents. Preface page ix. Overview 1. Queueing and loss networks 2. Decentralized optimization 4. Random access networks 5. Broadband networks 6. Internet modelling 8. Part I 11.

15 Aug 2012: revised 26 April 2002. Rigidity of the interface in percolationand random-cluster models. Guy Gielis1. Geoffrey Grimmett2. Abstract: We study conditioned random-cluster measures with edge-parameter pand cluster-weighting factor q satisfying q 1. The

15 Sep 2011: However,in the following section we discuss variations of the problem in which the op-timal policy does indeed lie within the class of partition policies.

22 Jul 2009: Donsker classes F. Our proofs will in fact show ‖P Wn Pn‖F = oP (1/.

15 Sep 2011: Appendix I contains a derivation of the op-timization problem of maximizing expected social welfare,and Appendix II justifies the fact that it can be solve usingLagrangian methods. ... APPENDIX IIJUSTIFICATION FOR USE OF LAGRANGIAN METHODS. We prove that

19 Nov 2010: Proof. Given ε > 0, apply Proposition 4 below with λ = ε so that ‖F Sn Fn‖ = oP (1/.

11 Sep 2008: n sup. f F. f (x)pn(x)d x. f (x)p0(x)d x. = OP(1), (3). ... supf F. |(Pn P)(µ̄n f f )| = oP(1/. n). The last two estimates prove (9) since F is P-Donsker.