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These proceedings contain selected papers presented at the Conference on Approximation, Probability and Related Fields held in Santa Barbara, California, on May 20-22, 1993. The main topics of the conference were: 1) approximation of functions by polynomials, splines, and operators, and applications to stochastics 2) numerical methods for approximation of deterministic and stochastic integrals 3) orthogonal polynomials and stochastic processes 4) positive linear operators and related deterministic and stochastic inequalities 5) multivariate approximation and interpolation 6) rate of convergence in probability theory 7) approximations and martingales 8) deterministic and stochastic inequalities 9) stability of deterministic and stochastic models 10) signal analysis 11) prediction theory 12) wavelets and approximations based on wavelets The Conference was very successful and received many compliments. We quote some of the letters sent by the participants: -"Many thanks for the wonderful conference and the exemplary organization!"
-"Many thanks for your good and effective work" We would like to thank the international organizing committee consisting of Paul Butzer, Stamatis Cambanis and Zuhair Nashed as well as the local organizing committee consisting of Bessy Athanasopoulos, Raisa Feldman, and Gleb Haynatzki for their superb work and for their contribution to the success of the Conference. The chairmer A ‾ C*p,. ‾lflIl", George Anastassiou Svetlozar Rachev ix CONTENTS 1. Preservation of Moduli of Continuity for Bernstein-type Operators ...Jose A. Adell and Jesus de la Cal 2. Lp-Korovkin Type Inequalities for Positive Linear Operators ...19 G. A. Anastassiou 3. On Some Shift-Invariant Integral Operators, Multivariate Case ...
Contents
1. Preservation of Moduli of Continuity for Bernstein-type Operators.- 2. Lp-Korovkin Type Inequalities for Positive Linear Operators.- 3. On Some Shift-Invariant Integral Operators, Multivariate Case.- 4. Multivariate Probabilistic Wavelet Approximation.- 5. Probabilistic Approach to the Rounding Problem with Applications to Fair Representation.- 6. Limit Theorems for Random Multinomial Forms.- 7. Multivariate Boolean Trapezoidal Rules.- 8. Convergence Results for an Extension of the Fourier Transform.- 9. Euler Functions E?(z) with Complex ? and Applications.- 10. On the Role of l? in Approximation Theory.- 11. The Action Constants.- 12. Bivariate Probability Distributions Similar to Exponential.- 13. Probability Waiting-Time Results for Pattern and Frequency Quotas in the Same Inverse Sampling Problem Via the Dirichlet.- 14. Asymptotic Normality of the Collision Resolution Interval for a Multiple Access Protocol.- 15. An Example of Non-Gaussian Density Process.- 16. Limit Theorems for Functionals of Markov Processes and Renormalizable Stable Fields.- 17. Stable Models in Testable Asset Pricing.- 18. A Note on the Death Process with a Random Parameter.- 19. Stochastic Approximation under Dependent Noises, Detecting Signals and Adaptive Control.- 20. Uniform Norm of Polynomials Constrained with Many Zeros in Two Disjoint Intervals.- 21. Admissible Location of Sample Points of Interpolation by Bivariate C1 Quadratic Splines.- 22. On a Bernstein-Type Operator of Bleimann, Butzer and Hahn III.- 23. A Problem of Analytic Monotone Extension in Three Dimensions.- 24. On the Joint Estimation of Stable Law Parameters.- 25. Representations and Properties of Geometric Stable Laws.- 26. Rearrangements of Conditionally Integrable Functions.- 27. Wavelet Transforms and WaveletApproximations.- 28. Approximations and Derivatives of Probability Functions.- 29. Rate of Convergence in the Central Limit Theorem for Generalized Convolutions.- 30. Order Completeness of L1 with Applications to Stochastics.- 31. On Reliability Analysis of Consecutive-k-out-of-n-F Systems and their Generalizations — A Survey.- 32. The Uniform Closure of Convex Semi-Lattices.- 33. Another Pairwise Independent, Stationary Chain.- 34. The Lebesgue Integral as an Improper Riemann Integral.- 35. Tests of Existence of Generalized Riemann Integrals.- 36. Remark on a Theorem About Polynomials.- Participants.
