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Asymptotic and Analytic Methods in Stochastic Evolutionary Symptoms
This book illustrates a number of asymptotic and analytic approaches applied for the study of random evolutionary systems, and considers typical problems for specific examples. In this case, constructive mathematical models of natural processes are used, which more realistically describe the trajectories of diffusion-type processes, rather than those of the Wiener process. We examine models where particles have some free distance between two consecutive collisions. At the same time, we investigate two cases: the Markov evolutionary system, where the time during which the particle moves towards some direction is distributed exponentially with intensity parameter λ; and the semi-Markov evolutionary system, with arbitrary distribution of the switching process. Thus, the models investigated here describe the motion of particles with a finite speed and the proposed random evolutionary process with characteristics of a natural physical process: free run and finite propagation speed. In the proposed models, the number of possible directions of evolution can be finite or infinite.
Modern Stochastics and Applications
This volume presents an extensive overview of all major modern trends in applications of probability and stochastic analysis. It will be a great source of inspiration for designing new algorithms, modeling procedures and experiments. Accessible to researchers, practitioners, as well as graduate and postgraduate students, this volume presents a variety of new tools, ideas and methodologies in the fields of optimization, physics, finance, probability, hydrodynamics, reliability, decision making, mathematical finance, mathematical physics and economics. Contributions to this Work include those of selected speakers from the international conference entitled “Modern Stochastics: Theory and Applications III,” held on September 10 –14, 2012 at Taras Shevchenko National University of Kyiv, Ukraine. The conference covered the following areas of research in probability theory and its applications: stochastic analysis, stochastic processes and fields, random matrices, optimization methods in probability, stochastic models of evolution systems, financial mathematics, risk processes and actuarial mathematics and information security.
Renewal Theory for Perturbed Random Walks and Similar Processes
This book offers a detailed review of perturbed random walks, perpetuities, and random processes with immigration. Being of major importance in modern probability theory, both theoretical and applied, these objects have been used to model various phenomena in the natural sciences as well as in insurance and finance. The book also presents the many significant results and efficient techniques and methods that have been worked out in the last decade. The first chapter is devoted to perturbed random walks and discusses their asymptotic behavior and various functionals pertaining to them, including supremum and first-passage time. The second chapter examines perpetuities, presenting results on c...
System Theory -- A Modern Approach, Volume 1
The theory of dynamic systems is addressed in this book in accordance with the “modern” approach, heir to algebraic analysis, which has been implemented since the last decade of the 20th century. After a reminder of the evolution of the representation of systems based on transfer functions or matrices, the duality of controllability and observability is revisited, and new results are produced concerning time-varying discrete-time systems. To complete and improve the existing analyses, the poles and zeros of linear systems and their interconnections are presented in a new way, as well as the problem of systems governed by functional differential equations (of retarded or neutral type) and their stabilization. This book also proposes known and original mathematical complements.
Mathematics and Philosophy 2
From Pythagoreans to Hegel, and beyond, this book gives a brief overview of the history of the notion of graphs and introduces the main concepts of graph theory in order to apply them to philosophy. In addition, this book presents how philosophers can use various mathematical notions of order. Throughout the book, philosophical operations and concepts are defined through examining questions relating the two kinds of known infinities – discrete and continuous – and how Woodin's approach can influence elements of philosophy. We also examine how mathematics can help a philosopher to discover the elements of stability which will help to build an image of the world, even if various approaches (for example, negative theology) generally cannot be valid. Finally, we briefly consider the possibilities of weakening formal thought represented by fuzziness and neutrosophic graphs. In a nutshell, this book expresses the importance of graphs when representing ideas and communicating them clearly with others.
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.
Introduction to Matrix-Analytic Methods in Queues 2
Matrix-analytic methods (MAM) were introduced by Professor Marcel Neuts and have been applied to a variety of stochastic models since. In order to provide a clear and deep understanding of MAM while showing their power, this book presents MAM concepts and explains the results using a number of worked-out examples. This book's approach will inform and kindle the interest of researchers attracted to this fertile field. To allow readers to practice and gain experience in the algorithmic and computational procedures of MAM, Introduction to Matrix-Analytic Methods in Queues 2 provides a number of computational exercises. It also incorporates simulation as another tool for studying complex stochastic models, especially when the state space of the underlying stochastic models under analytic study grows exponentially. This book's detailed approach will make it more accessible for readers interested in learning about MAM in stochastic models.
General Stochastic Measures
This book is devoted to the study of stochastic measures (SMs). An SM is a sigma-additive in probability random function, defined on a sigma-algebra of sets. SMs can be generated by the increments of random processes from many important classes such as square-integrable martingales and fractional Brownian motion, as well as alpha-stable processes. SMs include many well-known stochastic integrators as partial cases. General Stochastic Measures provides a comprehensive theoretical overview of SMs, including the basic properties of the integrals of real functions with respect to SMs. A number of results concerning the Besov regularity of SMs are presented, along with equations driven by SMs, types of solution approximation and the averaging principle. Integrals in the Hilbert space and symmetric integrals of random functions are also addressed. The results from this book are applicable to a wide range of stochastic processes, making it a useful reference text for researchers and postgraduate or postdoctoral students who specialize in stochastic analysis.
Introduction to Matrix Analytic Methods in Queues 1
Matrix-analytic methods (MAM) were introduced by Professor Marcel Neuts and have been applied to a variety of stochastic models since. In order to provide a clear and deep understanding of MAM while showing their power, this book presents MAM concepts and explains the results using a number of worked-out examples. This book’s approach will inform and kindle the interest of researchers attracted to this fertile field. To allow readers to practice and gain experience in the algorithmic and computational procedures of MAM, Introduction to Matrix Analytic Methods in Queues 1 provides a number of computational exercises. It also incorporates simulation as another tool for studying complex stochastic models, especially when the state space of the underlying stochastic models under analytic study grows exponentially. The book’s detailed approach will make it more accessible for readers interested in learning about MAM in stochastic models.
2000 American Alpine Journal
Published annually since 1929, The American Alpine Journal is internationally recognized as the world's finest journal of its kind. The latest volume of climbing's "journal of record" offers the most complete picture available of who did what in 1999. Conrad Anker relates the triumph and tragedy of the Mallory discovery high on the slopes of Mount Everest, while Renny Jackson and Valeri Babanov recount impressive Alaskan climbs, and Slovenian climbers report on the hardest and boldest climbs of the year. If it happened in the world of climbing, it's in the AAJ. Founded in 1902, the American Alpine Club is the leading national organization devoted to mountaineering and rock climbing, to the conservation and study of mountainous regions, and to representing the interests of the American climbing community. The AAC is based in Golden, Colorado.
