Bayesian analysis of complex models based on stochastic processes has in recent years become a growing area. This book provides a unified treatment of Bayesian analysis of models based on stochastic processes, covering the main classes of stochastic processing including modeling, computational, inference, forecasting, decision making and important applied models. Key features: Explores Bayesian analysis of models based on stochastic processes, providing a unified treatment. Provides a thorough introduction for research students. Computational tools to deal with complex problems are illustrated along with real life case studies Looks at inference, prediction and decision making. Researchers, graduate and advanced undergraduate students interested in stochastic processes in fields such as statistics, operations research (OR), engineering, finance, economics, computer science and Bayesian analysis will benefit from reading this book. With numerous applications included, practitioners of OR, stochastic modelling and applied statistics will also find this book useful.
This book was first published in 2004. Many observed phenomena, from the changing health of a patient to values on the stock market, are characterised by quantities that vary over time: stochastic processes are designed to study them. This book introduces practical methods of applying stochastic processes to an audience knowledgeable only in basic statistics. It covers almost all aspects of the subject and presents the theory in an easily accessible form that is highlighted by application to many examples. These examples arise from dozens of areas, from sociology through medicine to engineering. Complementing these are exercise sets making the book suited for introductory courses in stochastic processes. Software (available from www.cambridge.org) is provided for the freely available R system for the reader to apply to all the models presented.
1. A review of probability theory 2. Differential equations 3. Stochastic equations with Gaussian noise 4. Further properties of stochastic processes 5. Some applications of Gaussian noise 6. Numerical methods for Gaussian noise 7. Fokker-Planck equations and reaction-diffusion systems 8. Jump processes 9. Levy processes 10. Modern probability theory Appendix References Index.
Preface 1. Linear filtering theory 2. Optimal stochastic control for linear dynamic systems with quadratic payoff 3. Optimal control of linear stochastic systems with an exponential-of-integral performance index 4. Non linear filtering theory 5. Perturbation methods in non linear filtering 6. Some explicit solutions of the Zakai equation 7. Some explicit controls for systems with partial observation 8. Stochastic maximum principle and dynamic programming for systems with partial observation 9. Existence results for stochastic control problems with partial information References Index.
Generally, books on mathematical statistics are restricted to the case of independent identically distributed random variables. In this book however, both this case AND the case of dependent variables, i.e. statistics for discrete and continuous time processes, are studied. This second case is very important for today’s practitioners. Mathematical Statistics and Stochastic Processes is based on decision theory and asymptotic statistics and contains up-to-date information on the relevant topics of theory of probability, estimation, confidence intervals, non-parametric statistics and robustness, second-order processes in discrete and continuous time and diffusion processes, statistics for discrete and continuous time processes, statistical prediction, and complements in probability. This book is aimed at students studying courses on probability with an emphasis on measure theory and for all practitioners who apply and use statistics and probability on a daily basis.
Book on stochastic stability and control dealing with Liapunov function approach to study of Markov processes
MARTINGALE THEORY Covergence of Random Variables Conditioning Submartingales Convergence Theorems Optional Sampling of Closed Submartingale Sequences Maximal Inequalities for Submartingale Sequences Continuous Time Martingales Local Martingales Quadratic Variation The Covariation Process Semimartingales BROWNIAN MOTION Gaussian Process One Dimensional Brownian Motion STOCHASTIC INTEGRATION Measurability Properties of Stochastic Processes Stochastic Integration with Respect to Continuous Semimartingales Ito's Formula Change of Measure Representation of Continuous Local Martingales Miscellaneous APPLICATION TO FINANCE The Simple Black Scholes Market Pricing of Contingent Claims The General Market Model Pricing of Random Payoffs at Fixed Future Dates Interest Rate Derivatives APPENDIX Separation of Convex Sets The Basic Extension Procedure Positive Semidefinite Matrices Kolmogoroff Existence Theorem
Probability and Random Variables Introduction to Stochastic Processes Markov Chains Markov Chains in Continuous Time Diffusions Hints and solutions to selected exercises
Markov processes and their applications semimartingale theory and stochastic calculus white noise theory stochastic differential equations and its applications large deviations and applications a brief introduction to numerical analysis of (ordinary) stochastic differential equations without tears stochastic differential games and applications stability and stabilizing control of stochastic systems stochastic approximation - theory and applications stochastic manufacturing systems optimization by stochastic methods stochastic control methods in asset pricing.
This book covers the development of methods for detection and estimation of changes in complex systems. These systems are generally described by nonstationary stochastic models, which comprise both static and dynamic regimes, linear and nonlinear dynamics, and constant and time-variant structures of such systems. It covers both retrospective and sequential problems, particularly theoretical methods of optimal detection. Such methods are constructed and their characteristics are analyzed both theoretically and experimentally. Suitable for researchers working in change-point analysis and stochastic modelling, the book includes theoretical details combined with computer simulations and practical applications. Its rigorous approach will be appreciated by those looking to delve into the details of the methods, as well as those looking to apply them.
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