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Mechanics and Control of Solids and Structures
This book presents a collection of papers prepared by the researches of the Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences (IPME RAS) on the occasion of the 30th anniversary of the establishment of the Institute. The IPME RAS is one of the leading research institutes of the Russian Academy of Sciences and consists of 18 research units (laboratories). The chapters cover the main research directions of the institute, including nano-,micro-, meso- and macro- mechanics and materials, with ,special emphasis on the problems of strength of materials and service life of structures.
Recent Advances in Reliability Theory
This book presents thirty-one extensive and carefully edited chapters providing an up-to-date survey of new models and methods for reliability analysis and applications in science, engineering, and technology. The chapters contain broad coverage of the latest developments and innovative techniques in a wide range of theoretical and numerical issues in the field of statistical and probabilistic methods in reliability.
Random Motions in Markov and Semi-Markov Random Environments 2
This book is the second of two volumes on random motions in Markov and semi-Markov random environments. This second volume focuses on high-dimensional random motions. This volume consists of two parts. The first expands many of the results found in Volume 1 to higher dimensions. It presents new results on the random motion of the realistic three-dimensional case, which has so far been barely mentioned in the literature, and deals with the interaction of particles in Markov and semi-Markov media, which has, in contrast, been a topic of intense study. The second part contains applications of Markov and semi-Markov motions in mathematical finance. It includes applications of telegraph processes in modeling stock price dynamics and investigates the pricing of variance, volatility, covariance and correlation swaps with Markov volatility and the same pricing swaps with semi-Markov volatilities.
Earthquake Statistical Analysis through Multi-state Modeling
Earthquake occurrence modeling is a rapidly developing research area. This book deals with its critical issues, ranging from theoretical advances to practical applications. The introductory chapter outlines state-of-the-art earthquake modeling approaches based on stochastic models. Chapter 2 presents seismogenesis in association with the evolving stress field. Chapters 3 to 5 present earthquake occurrence modeling by means of hidden (semi-)Markov models and discuss associated characteristic measures and relative estimation aspects. Further comparisons, the most important results and our concluding remarks are provided in Chapters 6 and 7.
Fractional Brownian Motion
This monograph studies the relationships between fractional Brownian motion (fBm) and other processes of more simple form. In particular, this book solves the problem of the projection of fBm onto the space of Gaussian martingales that can be represented as Wiener integrals with respect to a Wiener process. It is proved that there exists a unique martingale closest to fBm in the uniform integral norm. Numerical results concerning the approximation problem are given. The upper bounds of distances from fBm to the different subspaces of Gaussian martingales are evaluated and the numerical calculations are involved. The approximations of fBm by a uniformly convergent series of Lebesgue integrals, semimartingales and absolutely continuous processes are presented. As auxiliary but interesting results, the bounds from below and from above for the coefficient appearing in the representation of fBm via the Wiener process are established and some new inequalities for Gamma functions, and even for trigonometric functions, are obtained.
Mathematics for Modeling and Scientific Computing
This book provides the mathematical basis for investigating numerically equations from physics, life sciences or engineering. Tools for analysis and algorithms are confronted to a large set of relevant examples that show the difficulties and the limitations of the most naïve approaches. These examples not only provide the opportunity to put into practice mathematical statements, but modeling issues are also addressed in detail, through the mathematical perspective.
Theory and Statistical Applications of Stochastic Processes
This book is concerned with the theory of stochastic processes and the theoretical aspects of statistics for stochastic processes. It combines classic topics such as construction of stochastic processes, associated filtrations, processes with independent increments, Gaussian processes, martingales, Markov properties, continuity and related properties of trajectories with contemporary subjects: integration with respect to Gaussian processes, Itȏ integration, stochastic analysis, stochastic differential equations, fractional Brownian motion and parameter estimation in diffusion models.
The Theory of Distributions
Many physical, chemical, biological and even economic phenomena can be modeled by differential or partial differential equations, and the framework of distribution theory is the most efficient way to study these equations. A solid familiarity with the language of distributions has become almost indispensable in order to treat these questions efficiently. This book presents the theory of distributions in as clear a sense as possible while providing the reader with a background containing the essential and most important results on distributions. Together with a thorough grounding, it also provides a series of exercises and detailed solutions. The Theory of Distributions is intended for master’s students in mathematics and for students preparing for the agrégation certification in mathematics or those studying the physical sciences or engineering.
Estimation of Stochastic Processes with Stationary Increments and Cointegrated Sequences
Estimation of Stochastic Processes is intended for researchers in the field of econometrics, financial mathematics, statistics or signal processing. This book gives a deep understanding of spectral theory and estimation techniques for stochastic processes with stationary increments. It focuses on the estimation of functionals of unobserved values for stochastic processes with stationary increments, including ARIMA processes, seasonal time series and a class of cointegrated sequences. Furthermore, this book presents solutions to extrapolation (forecast), interpolation (missed values estimation) and filtering (smoothing) problems based on observations with and without noise, in discrete and continuous time domains. Extending the classical approach applied when the spectral densities of the processes are known, the minimax method of estimation is developed for a case where the spectral information is incomplete and the relations that determine the least favorable spectral densities for the optimal estimations are found.
Structural Equation Modeling with lavaan
This book presents an introduction to structural equation modeling (SEM) and facilitates the access of students and researchers in various scientific fields to this powerful statistical tool. It offers a didactic initiation to SEM as well as to the open-source software, lavaan, and the rich and comprehensive technical features it offers. Structural Equation Modeling with lavaan thus helps the reader to gain autonomy in the use of SEM to test path models and dyadic models, perform confirmatory factor analyses and estimate more complex models such as general structural models with latent variables and latent growth models. SEM is approached both from the point of view of its process (i.e. the different stages of its use) and from the point of view of its product (i.e. the results it generates and their reading).
