On Existence of Solutions of Semilinear Impulsive Functional Differential Equations with Nonlocal Conditions -- On Banach-Lie Algebras, Spectral Decompositions and Complex Polarizations -- Commuting Triples of Subnormal Operators and Related Moment Problems -- The Equality of the Reduced and the Full C*-Algebras and the Amenability of a Topological Groupoid -- ?-Numerical Radius in Banach Space…
Modeling Text Databases -- An Overview of Probabilistic and Time Series Models in Finance -- Stereological Estimation of the Rose of Directions from the Rose of Intersections -- Approximations for Multiple Scan Statistics -- Krawtchouk Polynomials and Krawtchouk Matrices -- An Elementary Rigorous Introduction to Exact Sampling -- On the Different Extensions of the Ergodic Theorem of Information…
Lévy Processes in Euclidean Spaces and Groups -- Locally Compact Quantum Groups -- Quantum Stochastic Analysis - an Introduction -- Dilations, Cocycles and Product Systems.This volume is the first of two volumes containing the revised and completed notes lectures given at the school "Quantum Independent Increment Processes: Structure and Applications to Physics". This school was held at the Al…
Introductory Measure Theory -- Random Variables -- Inequalities -- Characteristic Functions -- Convergence -- The Law of Large Numbers -- The Central Limit Theorem -- The Law of the Iterated Logarithm -- Limit Theorems; Extensions and Generalizations -- Martingales."I know it’s trivial, but I have forgotten why". This is a slightly exaggerated characterization of the unfortunate attitude of m…
Why probability and statistics? -- Outcomes, events, and probability -- Conditional probability and independence -- Discrete random variables -- Continuous random variables -- Simulation -- Expectation and variance -- Computations with random variables -- Joint distributions and independence -- Covariance and correlation -- More computations with more random variables -- The Poisson process -- …
Motivating Studies -- Generalized Linear Models -- Linear Mixed Models for Gaussian Longitudinal Data -- Model Families -- The Strength of Marginal Models -- Likelihood-based Marginal Models -- Generalized Estimating Equations -- Pseudo-Likelihood -- Fitting Marginal Models with SAS -- Conditional Models -- Pseudo-Likehood -- From Subject-specific to Random-effects Models -- The Generalized Lin…
Pricing by Arbitrage -- Martingale Measures -- The First Fundamental Theorem -- Complete Markets -- Discrete-time American Options -- Continuous-Time Stochastic Calculus -- Continuous-Time European Options -- The American Put Option -- Bonds and Term Structure -- Consumption-Investment Strategies -- Measures of Risk.This book presents the mathematics that underpins pricing models for derivative…
Assessment of characteristic shear strength parameters of soil and its implication in geotechnical design -- Ambiguity of safety definition in geotechnical models -- The fuzziness and sensitivity of failure probabilities -- The mathematics of uncertainty: models, methods and interpretations -- Multi-parameter models: rules and computational methods for combining uncertainties -- Sensitivity ana…
Spot and Futures Markets -- An Introduction to Financial Derivatives -- Discrete-time Security Markets -- Benchmark Models in Continuous Time -- Foreign Market Derivatives -- American Options -- Exotic Options -- Volatility Risk -- Continuous-time Security Markets -- Fixed-income Markets -- Interest Rates and Related Contracts -- Short-Term Rate Models -- Models of Instantaneous Forward Rates -…
Markov Process -- Basic Properties -- Hunt Process -- Brownian Motion -- Potential Developments -- Generalities -- Markov Chains: a Fireside Chat -- Ray Processes -- Application to Markov Chains -- Time Reversal -- h-Transforms -- Death and Transfiguration: A Fireside Chat -- Processes in Duality -- The Martin Boundary -- The Basis of Duality: A Fireside Chat.From the reviews of the First Editi…