The Theory of Stochastic Processes i

The dynamic behaviour of novel and complicated structures often needs to be investigated by system analysis and system identification, since it usually has to meet certain requirements. A priori knowledge concerning the real system is gained by system analysis and/or previous tests, and it results in a non-parametric and/or in a parametric mathematical model. The identification of system parameters, i.e. experimental system analysis, is performed using measured quantities and taking into account deterministic and stochastic errors. If results of the identification have to be compared with the results of the system analysis, and if certain error bounds are exceeded, the model has to be improved. System identification has to take into account random aspects (errors, test signals), the real dynamic behaviour (damping coupling, non-linearities) and questions concerning practical handling (including large systems, economics). A broad understanding of system identification needs as its basis an extended theory of structural vibrations and estimation (stochastic processes), and must be coupled with practical aspects including experience and validated software.

From his unique perspective, renowned statistician and educator Frederick Mosteller describes many of the projects and events in his long career. From humble beginnings in western Pennsylvania to becoming the founding chairman of Harvard University’s Department of Statistics and beyond, he inspired many statisticians, scientists, and students with his unabashed pragmatism, creative thinking, and zest for both learning and teaching. This candid account offers fresh insights into the qualities that made Mosteller a superb teacher, a prolific scholar, a respected leader, and a valued advisor.

The book presents a general overview of mathematical models in the context of evolution. It covers a wide range of topics such as population genetics, population dynamics, speciation, adaptive dynamics, game theory, kin selection, and stochastic processes. Written by leading scientists working at the interface between evolutionary biology and mathematics the book is the outcome of a conference commemorating Charles Darwin's 200th birthday, and the 150th anniversary of the first publication of his book "On the origin of species".

Authors: Davey, S., Gordon, N., Holland, I., Rutten, M., Williams, J.
Presents a unique insight into the Bayesian calculation of the search zone for MH370
Written by members of the MH370 search team
Contains a tutorial description of available data allowing readers to work out their own solutions

This book presents Markov and quantum processes as two sides of a coin called generated stochastic processes. It deals with quantum processes as reversible stochastic processes generated by one-step unitary operators, while Markov processes are irreversible stochastic processes generated by one-step stochastic operators. The characteristic feature of quantum processes are oscillations, interference, lots of stationary states in bounded systems and possible asymptotic stationary scattering states in open systems, while the characteristic feature of Markov processes are relaxations to a single stationary state.

This is a complete update of the first edition of Level Crossing Methods in Stochastic Models, which was published in 2008. Level crossing methods are a set of sample-path based mathematical tools used in applied probability to establish reliable probability distributions.

Stochastic Calculus for Finance evolved from the first ten years of the Carnegie Mellon Professional Master's program in Computational Finance. The content of this book has been used successfully with students whose mathematics background consists of calculus and calculus-based probability. The text gives both precise statements of results, plausibility arguments, and even some proofs, but more importantly intuitive explanations developed and refine through classroom experience with this material are provided. The book includes a self-contained treatment of the probability theory needed for stochastic calculus, including Brownian motion and its properties. Advanced topics include foreign exchange models, forward measures, and jump-diffusion processes.

This volume presents selected and peer-reviewed contributions from the 14th Workshop on Stochastic Models, Statistics and Their Applications, held in Dresden, Germany, on March 6-8, 2019. Addressing the needs of theoretical and applied researchers alike, the contributions provide an overview of the latest advances and trends in the areas of mathematical statistics and applied probability, and their applications to high-dimensional statistics, econometrics and time series analysis, statistics for stochastic processes, statistical machine learning, big data and data science, random matrix theory, quality control, change-point analysis and detection, finance, copulas, survival analysis and reliability, sequential experiments, empirical processes, and microsimulations.