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Adaptive Statistical Procedures and Related Topics || Constrained Stochastic Approximation via the Theory of Large Deviations

✍ Scribed by H. Kushner and P. Dupuis

Book ID: 124984418
Publisher: Institute of Mathematical Statistics
Year: 1986
Weight: 748 KB
Volume: 8
Category: Article
ISSN: 0749-2170
DOI: 10.2307/4355536

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Let G be a bounded convex set, and H G the projection onto G, and {~j} a bounded random process. Projected algorithms of the types X~ + 1 = H~(X~ + ~ b (X~, ~,)) (or X n + 1 = He(X, + a, b (Xn, in)), where 0 < a n ~ 0, Z a, = oo) occur frequently in applications (among other places) in control and c

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Communication Systems and Techniques Volume 747 || Appendix A. The Q Function and Related IntegralsThis Appendix is largely adapted from S. Stein, The QFunction and Related Integrals, Research Report 467, Applied Research Laboratory, Sylvania Electronic Systems, July, 1965.The Q function was introduced in: J. I. Marcum, A Statistical Theory of Target Detection by Pulsed Radar, IRE Trans. Inform. Theory, vol. IT6, pp. 59267, April, 1960; earlier Rand Corp. Res. Memos RM753, July, 1948 and RM754, December, 1947; J. I. Marcum, Tables of the Qfunction, Rand Corp. Res. Memo RM399, January, 1950.Examples of literature on machine computation of the Q function are: A. R. DiDonato and M. P. Jarnagin, A Method for Computing the Circular Coverage Function, Mathematics of Computation, vol. 16, pp. 347355, July, 1962; D. E. Johansen, New Techniques for Machine Computation of the Qfunctions, Truncated Normal Deviates, and Matrix Eigenvalues, Applied Research Laboratory, Sylvania Electronic Systems, AFCRL556, July, 1961.

✍ Schwartz, Mischa; Bennett, William R.; Stein, Seymour 📂 Article 📅 2009 🏛 IEEE ⚖ 455 KB