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

This textbook presents some basic stochastic processes, mainly Markov processes. It begins with a brief introduction to the framework of stochastic processes followed by the thorough discussion on Markov chains, which is the simplest and the most important class of stochastic processes. The book then elaborates the theory of Markov chains in detail including classification of states, the first passage distribution, the concept of periodicity and the limiting behaviour of a Markov chain in terms of associated stationary and long run distributions. The book first illustrates the theory for...

This book focuses on research in linear algebra, statistics, matrices, graphs and their applications. Many chapters in the book feature new findings due to applications of matrix and graph methods. The book also discusses rediscoveries of the subject by using new methods. Dedicated to Prof. Calyampudi Radhakrishna Rao (C.R. Rao) who has completed 100 years of legendary life and continues to inspire us all and Prof. Arbind K. Lal who has sadly departed us too early, it has contributions from collaborators, students, colleagues and admirers of Professors Rao and Lal. With many chapters on...

This book is devoted to real analysis methods for the problem of constructing Markov processes with boundary conditions in probability theory. Analytically, a Markovian particle in a domain of Euclidean space is governed by an integro-differential operator, called the Waldenfels operator, in the interior of the domain, and it obeys a boundary condition, called the Ventcel (Wentzell) boundary condition, on the boundary of the domain. Most likely, a Markovian particle moves both by continuous paths and by jumps in the state space and obeys the Ventcel boundary condition, which consists of...

This book explains the importance of using the probability that the hypothesis is correct (PHC), an intuitive measure that anyone can understand, as an alternative to the p-value. In order to overcome the "reproducibility crisis" caused by the misuse of significance tests, this book provides a detailed explanation of the mechanism of p-hacking using significance tests, and concretely shows the merits of PHC as an alternative to p-values.

In March 2019, two impactful papers on statistics were published. One paper, "Moving to a World Beyond 'p <...

This textbook presents some basic stochastic processes, mainly Markov processes. It begins with a brief introduction to the framework of stochastic processes followed by the thorough discussion on Markov chains, which is the simplest and the most important class of stochastic processes. The book then elaborates the theory of Markov chains in detail including classification of states, the first passage distribution, the concept of periodicity and the limiting behaviour of a Markov chain in terms of associated stationary and long run distributions. The book first illustrates the theory for...

The area of Reliability has become a very important and active area of research. This is clearly evident from the large body of literature that has been developed in the form of books, volumes and research papers since 1988 when the previous Handbook of Statistics on this area was prepared by P.R. Krishnaiah and C.R. Rao. This is the reason we felt that this is indeed the right time to dedicate another volume in the Handbook of Statistics series to highlight some recent advances in the area of Reliability. With this purpose in mind, we solicited articles from leading experts working in the...

The chapters fall into four groups. The first four cover the fundamentals of stochastic processes, and lay the foundation...

Nonlinear Dynamical Systems and Control presents and develops an extensive treatment of stability analysis and control design of nonlinear dynamical systems, with an emphasis on Lyapunov-based methods. Dynamical system theory lies at the heart of mathematical sciences and engineering. The application of dynamical systems has crossed interdisciplinary boundaries from chemistry to biochemistry to chemical kinetics, from medicine to biology to population genetics, from economics to sociology to psychology, and from physics to mechanics to engineering. The increasingly complex...