Modeling Uncertainty

Cover -- Contents -- Preface -- Contributing Authors -- 1 Professor Sidney J. Yakowitz -- Part I -- 2 Stability of Single Class Queueing Networks -- 1 Introduction -- 2 The Model -- 3 Stability: Introduction -- 4 Perturbed Liapunov Functions -- 5 Stability -- 3 Sequential Optimization Under Uncertainty -- 1 Introduction -- 2 Bandit Theory -- 3 Adaptive Control of Markov Chains -- 4 Stochastic Approximation -- 4 Exact Asymptotics for Large Deviation Probabilities, with Applications -- 1 Limit Theorems on the last negative sum and applications to nonparametric bandit theory -- 2 Large deviations in a space of trajectories -- 3 Asymptotic equivalence of the tail of the sum of independent random vectors and the tail of their maximum -- Part II -- 5 Stochastic Modelling of Early HIV Immune Responses Under Treatment by Protease Inhibitors -- 1 Introduction -- 2 A Stochastic Model of Early HIV Pathogenesis Under Treatment by a Protease Inbihitor -- 3 Mean Values of U(T)={T*(T), V0(T), V1(T)} -- 4 A State Space Model for the Early HIV Pathogenesis Under Treatment by Protease Inhibitors -- 5 An Example Using Real Data -- 6 Some Monte Carlo Studies -- 6 The impact of re-using hypodermic needles -- 1 Introduction -- 2 Geometric distribution with variable success probability -- 3 Validity of the distribution -- 4 Mean and variance of I -- 5 Intensity of epidemic -- 6 Reducing infection -- 7 The spread of the Ebola virus in 1976 -- 8 Conclusions -- 7 Nonparametric Frequency Detection and Optimal Coding in Molecular Biology -- 1 Introduction -- 2 The Spectral Envelope -- 3 Sequence Analyses -- 4 Discussion -- Part III -- 8 An Efficient Stochastic Approximation Algorithm for Stochastic Saddle Point Problems -- 1 Introduction -- 2 Stochastic saddle point problem -- 3 Discussion -- 4 Numerical Results -- 5 Conclusions -- Appendix: A: Proof of Theorems 1 and 2 -- Appendix: B: Proof of the Proposition -- 9 Regression Models for Binary Time Series -- 1 Introduction -- 2 Partial Likelihood Inference -- 3 Goodness of Fit -- 4 Logistic Regression -- 5 Categorical Data -- 10 Almost Sure Convergence Properties of Nadaraya-Watson Regression Estimates -- 1 Introduction -- 2 Results -- 3 Lemmas and Proofs -- 11 Strategies for Sequential Prediction of Stationary Time Series -- 1 Introduction -- 2 Universal prediction by partitioning estimates -- 3 Universal prediction by generalized linear estimates -- 4 Prediction of Gaussian processes -- Part IV -- 12 The Birth of Limit Cycles in Nonlinear Oligopolies with Continuously Distributed Information Lag -- 1 Introduction -- 2 Nonlinear Oligopoly Models -- 3 The Dynamic Model with Lag Structure -- 4 Bifurcation Analysis in the General Case -- 5 The Symmetric Case -- 6 Special Oligopoly Models -- 7 Conclusions -- 13 A Differential Game of Debt Contract Valuation -- 1 Introduction -- 2 The firm and the debt contract -- 3 A stochastic game -- 4 Equivalent risk neutral valuation -- 5 Debt and Equity valuations for Nash equilibrium strategies.