Kategoria BISAC: Mathematics >> Probability & Statistics - Stochastic Processes

This book explores regime-switching Brownian motion, a class of stochastic processes widely used in fields such as mathematical finance, risk theory, queueing theory, and epidemiological modeling. These processes are studied within the Markovian regime-switching framework, which captures dynamic environments characterized by shifts between different states or "regimes" for example, economic cycles, seasonal environmental variations, or short-term surges in activity.

The matrix-analytic approach, introduced approximately fifty years ago in the context of classical queueing theory,...

This book does not focus solely on asymptotic extreme value distributions. In addition to the traditional asymptotic methods, it introduces a data-driven, computer-based method, which provides insights into the exact extreme value distribution inherent in the data, and which avoids asymptotics. It therefore differs from currently available texts on extreme value statistics in one very important aspect.  The method described provides a unique tool for diagnostics, and for efficient and accurate extreme value prediction based on measured or simulated data. It also has straightforward...

This book on asymptotic and methodological statistics celebrates the distinguished career of Marie Hu ková and her foundational work in modern mathematical statistics. It brings together original research contributions from renowned statisticians, focusing on asymptotic theory, methodological innovations, and applications in statistical inference. The volume highlights cutting-edge developments in change-point analysis, goodness-of-fit testing and nonparametric statistics, reflecting the extensive impact Marie Hu ková has had in shaping the direction of contemporary statistical science....

• Clear, readable style
• Solutions to many problems presented in text
• Solutions manual for instructors
• Material new to the second edition on ergodic theory, Brownian motion, and convergence theorems used in...

- New probabilistic model, new results in probability theory
- Original applications in computer science
- Applications in mathematical physics
- Applications in finance

A cornerstone of applied probability, Markov chains can be used to help model how plants grow, chemicals react, and atoms diffuse--and applications are increasingly being found in such areas as engineering, computer science, economics, and education. To apply the techniques to real problems, however, it is necessary to understand how Markov chains can be solved numerically. In this book, the first to offer a systematic and detailed treatment of the numerical solution of Markov chains, William Stewart provides scientists on many levels with the power to put this theory to use in the actual...

Based on lectures in Erevan, this exposition of ergodic theory contains a rich collection of examples well chosen to introduce the reader to the main themes of the subject. Topics discussed include existence of invariant measures, geodesic flows on Riemannian manifolds, ergodic theory of an ideal gas, and entropy of dynamical systems.

Kiyosi Ito's greatest contribution to probability theory may be his introduction of stochastic differential equations to explain the Kolmogorov-Feller theory of Markov processes. Starting with the geometric ideas that guided him, this book gives an account of Ito's program.

The modern theory of Markov processes was initiated by A. N. Kolmogorov. However, Kolmogorov's approach was too analytic to reveal the probabilistic foundations on which it rests. In particular, it hides the central role played by the simplest Markov processes: those with independent, identically distributed...

This book deals with the tools and techniques used in the stochastic process - estimation, optimisation and recursive logarithms - in a form accessible to engineers and which can also be applied to Matlab.

Amongst the themes...