“…Essential for undergraduate students, PhD students, and instructors, the problems in this book vary in difficulty and cover most of the obligatory courses given at the undergraduate level, including calculus, algebra, geometry, discrete mathematics, measure theory, complex analysis, differential equations, and probability theory. Detailed solutions to all of the problems from Part I are supplied in Part II, giving students the ability to check their solutions and observe new and unexpected ideas. …”
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“…This kind of duality, having emerged from manifolds of probability distributions, is ubiquitous, appearing in a variety of problems which might have no explicit relation to probability theory. Through the duality, it is possible to analyze various fundamental problems in a unified perspective. …”
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“…One of the most active areas of research in summability theory is the concept of statistical convergence, which is a generalization of the familiar and widely investigated concept of convergence of real and complex sequences, and it has been used in Fourier analysis, probability theory, approximation theory and in other branches of mathematics. …”
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“…It also features a comprehensive appendix covering the prerequisites in probability theory, matrix algebra, mathematical calculus, and numerical analysis, and each chapter is complemented by exercises. …”
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“…Measure theory and integration are presented to undergraduates from the perspective of probability theory. The first chapter shows why measure theory is needed for the formulation of problems in probability, and explains why one would have been forced to invent Lebesgue theory (had it not already existed) to contend with the paradoxes of large numbers. …”
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“…It will also appeal to researchers in probability theory who seek an authoritative reference on stable distributions.…”
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“…The volume presents extensive research devoted to a broad spectrum of mathematical analysis and probability theory. Subjects discussed in this Work are those treated in the so-called Strasbourg–Zürich Meetings. …”
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“…In probability theory and statistics, it is customary to employ unit distributions to explain practical variables having values between zero and one. …”
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“…A solid understanding of the fundamental concepts of probability theory is becoming essential to the rational interpretation of medical information. …”
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“…Our goal is to present a well-known rigorous probabilistic framework in which to study these equations in a way that is accessible to practitioners currently working in the area, and thus to bridge some of the cultural/scientific gaps between probability theory and mathematical biology. In this way, the paper is intended to act as a reference that collects together relevant rigorous results about notions of solutions and well-posedness, which although may be straightforward to experts from SPDEs, are largely unknown in the neuroscientific community, and difficult to find in a very large body of literature. …”
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“…The discussion about the parameters corresponding with geometry and material property was accomplished by probability theory and mathematical statistics.…”
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“…Firstly, according to the probability theory, we derive the calculation method for the expectation of the coverage quality with multiple joint nodes, which aims to reduce the coverage blind area and improving network coverage rate. …”
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“…Rough random theory, generally applied to statistics, decision-making, and so on, is an extension of rough set theory and probability theory, in which a rough random variable is described as a random variable taking “rough variable” values. …”
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“…Rationality in human decision making under uncertainty is normatively prescribed by the axioms of probability theory in order to maximize utility. However, substantial literature from psychology and cognitive science shows that human decisions regularly deviate from these axioms. …”
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“…Hungar. 1962, 3, 188–198], and the constraint of maintaining a desired marginal distribution is similar to coupling in probability theory. Using our Fano-type inequalities for Shannon’s and Rényi’s information measures, we also investigate the asymptotic behavior of the sequence of Shannon’s and Rényi’s equivocations when the error probabilities vanish. …”
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“…The aim of this paper is to present new mathematical concepts that are based on information and probability theory and can be applied to network analysis in Team Sports. …”
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“…This volume will be a useful addition to the libraries both of wireless communication students and those studying probability theory.…”
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“…To achieve these objectives Stochastic Systems presents: ·         A clear and brief review of essential concepts on probability theory, random functions, stochastic calculus, Monte Carlo simulation, and functional analysis   ·          Probabilistic models for random variables and functions needed to formulate stochastic equations describing realistic problems in engineering and applied sciences   ·          Practical methods for quantifying the uncertain parameters in the definition of stochastic equations, solving approximately these equations, and assessing the accuracy of approximate solutions   Stochastic Systems provides key information for researchers, graduate students, and engineers who are interested in the formulation and solution of stochastic problems encountered in a broad range of disciplines. …”
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“…Nevertheless, the reader should be familiar with the most important concepts of statistics and probability theory albeit two appendices have been dedicated to provide a rudimentary discussion.…”
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“…The purpose of the conference was to represent recent developments in measure theoretic, differentiable and topological dynamical systems as well as connections to probability theory, stochastic processes, operator theory and statistical physics. …”
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