Overview and Basic Facts -- Gaussian Processes and Related Structures -- Matching Theorems -- The Bernoulli Conjecture -- Families of distances -- Applications to Banach Space Theory.Author's Note: The material of this book has been reworked and expanded with a lot more detail and published in the author's 2014 book "Upper and Lower Bounds for Stochastic Processes" (Ergebnisse Vol. 60, ISBN 978…
An Overview of the Book -- Optimal Markovian Couplings -- New Variational Formulas for the First Eigenvalue -- Generalized Cheeger’s Method -- Ten Explicit Criteria in Dimension One -- Poincaré-Type Inequalities in Dimension One -- Functional Inequalities -- A Diagram of Nine Types of Ergodicity -- Reaction-Diffusion Processes -- Stochastic Models of Economic Optimization.A problem of broad …
Preface -- Markovian Jump Linear Systems -- Background Material -- On Stability -- Optimal Control -- Linear Filtering -- Quadratic Optimal Control with Partial Information -- H2- Control -- Design Techniques and Examples -- Appendix A: Coupled Algebraic Riccati Equations -- Appendix B: Auxiliary Results for the Linear Filtering Problem with (k) Unknown -- Appendix C: Auxiliary Results for the …
Prologue and Preliminaries -- Introduction, Overview, and Examples -- Mathematical Preliminaries -- Asymptotic Properties -- Asymptotic Expansions -- Occupation Measures -- Exponential Bounds -- Interim Summary and Extensions -- Applications -- Stability of Dynamic Systems -- Filtering -- Markov Decision Processes -- LQ Controls -- Mean-Variance Controls -- Production Planning -- Stochastic App…
to Option Pricing -- Asset Pricing Basics -- Continuous-Time Models -- Black-Scholes -- Estimating and Modelling Volatility -- to Monte Carlo and Binomial Models -- Advanced Option Pricing -- Foreign Exchange -- Forward, Futures, and Exchange Options -- Exotic Options -- More on Monte Carlo and Binomial Valuation -- Finite Difference Methods -- Fixed Income -- Fixed Income Concepts -- to Fixed …
Part I. Probability. Basic Notions, Structure, Methods: Introduction; The Probability Space; Independence; General Theory of Stochastic Processes and Random Functions; Limit Theorems -- Part II. Markov Processes and Probability Applications in Analysis: Markov Processes; Probabilistic Representations of Solutions of Partial Differential Equations; Wiener Process and the Solution of Equations In…
and Models of Manufacturing Systems -- Concept of Near—Optimal Control -- Models of Manufacturing Systems -- Optimal Control of Manufacturing Systems: Existence and Characterization -- Optimal Control of Parallel—Machine Systems -- Optimal Control of Dynamic Flowshops -- Optimal Controls of Dynamic Jobshops -- Risk-Sensitive Control -- Near—Optimal Controls -- Near—Optimal Control of Pa…
Stochastic Calculus with Jump diffusions -- Optimal Stopping of Jump Diffusions -- Stochastic Control of Jump Diffusions -- Combined Optimal Stopping and Stochastic Control of Jump Diffusions -- Singular Control for Jump Diffusions -- Impulse Control of Jump Diffusions -- Approximating Impulse Control of Diffusions by Iterated Optimal Stopping -- Combined Stochastic Control and Impulse Control …
Matrix Preliminaries and General Linear Model -- Some General Methods for Making Inferences about Variance Components -- One-Way Classification -- Two-Way Crossed Classification without Interaction -- Two-Way Crossed Classification with Interaction -- Three-Way and Higher-Order Crossed Classifications -- Two-Way Nested Classification -- Three-Way Nested Classification -- General r-Way Nested Cl…
Multivariate Data and Multivariate Analysis -- Looking at Multivariate Data -- Principal Components Analysis -- Exploratory Factor Analysis -- Multidimensional Scaling and Correspondence Analysis -- Cluster Analysis -- Grouped Multivariate Data: Multivariate Analysis of Variance and Discriminant Function Analysis -- Multiple Regression and Canonical Correlation -- Analysis of Repeated Measures …