Random Closed Sets and Capacity Functionals -- Expectations of Random Sets -- Minkowski Addition -- Unions of Random Sets -- Random Sets and Random Functions. Appendices: Topological Spaces -- Linear Spaces -- Space of Closed Sets -- Compact Sets and the Hausdorff Metric -- Multifunctions and Continuity -- Measures and Probabilities -- Capacities -- Convex Sets -- Semigroups and Harmonic Analys…
Theory -- Model-Based Approaches -- QMP-ZPC Filters -- The Periodogram -- Direct Filter Approach (DFA) -- Finite Sample Problems and Regularity -- Empirical Results -- Empirical Comparisons : Mean Square Performance -- Empirical Comparisons : Turning Point Detection -- Conclusion.The material contained in this book originated in interrogations about modern practice in time series analysis. • …
Overview of Geometric Data Analysis (‘Overview’) -- Correspondence Analysis -- Euclidean Cloud -- Principal Component Analysis -- Multiple Correspondence Analysis (MCA) -- Structured Data Analysis -- Stability of a Euclidean Cloud -- Inductive Data Analysis -- Research Case Studies -- Mathematical Bases.Geometric Data Analysis (GDA) is the name suggested by P. Suppes (Stanford University) t…
The reversal of particularity and generality in economics -- Konnyaku Mondo and Game Theory -- The market economy in a rage -- Decision making and Nash equilibrium -- The individual and society.This book consists of five acts and two interludes, which are all written as dialogues between three main characters and other supporting characters. Each act discusses the epistemological, institutional…
Stability of dynamical systems, bifurcations, and generic properties -- Discrete invariants of dynamical systems -- Entropy and topological aspects of dynamical systems -- Entropy and metric aspects of dynamical systems -- Entropy and measure theoretic aspects of dynamical systems -- Smooth dynamical systems -- Cellular automata and Boolean networks as examples of discrete dynamical systems.Our…
Repeated and Stochastic Games -- Information and the Existence of Stationary Markovian Equilibrium -- Markov Games under a Geometric Drift Condition -- A Simple Two-Person Stochastic Game with Money -- New Approaches and Recent Advances in Two-Person Zero-Sum Repeated Games -- Notes on Risk-Sensitive Nash Equilibria -- Continuous Convex Stochastic Games of Capital Accumulation -- Differential D…
Basic Information on Capital Markets -- Random Walks in Finance and Physics -- The Black-Scholes Theory of Option Prices -- Scaling in Financial Data and in Physics -- Turbulence and Foreign Exchange Markets -- Derivative Pricing Beyond Black—Scholes -- Microscopic Market Models -- Theory of Stock Exchange Crashes -- Risk Management -- Economic and Regulatory Capital for Financial Institution…
Mathematical Symbols and Constants -- Sets and Propositions -- Number Systems and their Arithmetic -- Combinatorial Analysis -- Sequences and Series -- Mathematics of Finance -- Functions of one Independent Variable -- Functions of one Variable: Differential Calculus -- Functions of one Variable: Integral Calculus -- Differential Equations -- Difference Equations -- Differential Calculus for Fu…
Performance Analysis Techniques -- Convexity and Supermodularity -- Worst-Case Analysis -- Average-Case Analysis -- Mathematical Programming Based Bounds -- Inventory Models -- Economic Lot Size Models with Constant Demands -- Economic Lot Size Models with Varying Demands -- Stochastic Inventory Models -- Integration of Inventory and Pricing -- Design and Coordination Models -- Procurement Cont…
Eqilibrium Components with Arbitrary Index -- A Reformulation of the Index for Equilibria in Bimatrix Games -- Sperner’s Lemma and Labelling Theorems -- A Strategic Characterisation of the Index -- Outside Option Equilibrium Components -- Index Zero and Hyperstability.