“…Graduate students in applied mathematics with an understanding of probability theory and stochastic calculus will find this book useful to gain a deeper understanding of fundamental concepts and methods in mathematical finance.…”
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“…This book provides a detailed introduction to the key concepts used in processing quantum information and reveals that quantum mechanics is a generalisation of classical probability theory. The second edition contains new sections and entirely new chapters: the hot topic of multipartite entanglement; in-depth discussion of the discrete structures in finite dimensional Hilbert space, including unitary operator bases, mutually unbiased bases, symmetric informationally complete generalized measurements, discrete Wigner function, and unitary designs; the Gleason and Kochen-Specker theorems; the proof of the Lieb conjecture; the measure concentration phenomenon; and the Hastings' non-additivity theorem. …”
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“…It begins with a review of classical probability theory and quantum theory, as well as a careful discussion of the notions of information and entropy, prior to embarking on the development of statistical physics proper. …”
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“…Until recently, probability theory offered no tools to help answer such questions. …”
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“…First-passage percolation (FPP) is a fundamental model in probability theory that has a wide range of applications to other scientific areas (growth and infection in biology, optimization in computer science, disordered media in physics), as well as other areas of mathematics, including analysis and geometry. …”
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“…It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. …”
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“…The prerequisites are an elementary knowledge of mechanics, probability theory and functional analysis.…”
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“…Researchers and graduate student in probability theory will find this book very useful.…”
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“…Contents Optimal Control of Markov Processes A Singular Stochastic Control Problem Dynamic Programming Approach and Consequences Target Groups Researchers and students in the fields of mathematics, probability theory and applied mathematics in financial and actuarial industry Mathematicians from the financial and actuarial industry The Author Josef Anton Strini wrote his master’s thesis under the supervision of Prof. …”
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“…It provides a new viewpoint from which one can examine various aspects of representation theory and areas of application, such as probability theory and harmonic analysis. For example, the focal objects of this book, group matrices, can be thought of as a generalization of the circulant matrices which are behind many important algorithms in information science. …”
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“…Basic notions from probability theory are introduced. Executable code examples are included to enhance the book’s practical use for scientific modellers, and all code is available online as well.…”
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“…This numerical algorithm is utilized to compute copy number variation and the associated statistical confidence interval and is based on results from probability theory and statistics. We also provide formulas which can be used as close approximations.…”
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“…We address two sets of long-standing open questions in linear algebra and probability theory, from a computational complexity perspective: stochastic matrix divisibility, and divisibility and decomposability of probability distributions. …”
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“…Problems of such diversity cannot be placed within a single traditional scientific discipline, but call for the expertise in probability theory for quantifying the cause, interaction problems for better understanding the physical nature of the problems, as well as modeling and computational techniques for improving the representation of inelastic behavior mechanisms and providing the optimal design.…”
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“…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. …”
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“…Although analytic results have been presented previously in various monographs on zeta-functions, this is the first book containing both analytic and probability theory of Lerch zeta-functions. The book starts with classical analytical theory (Euler gamma-functions, functional equation, mean square). …”
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“…The goal of this Lecture Note is to prove a new type of limit theorems for normalized sums of strongly dependent random variables that play an important role in probability theory or in statistical physics. Here non-linear functionals of stationary Gaussian fields are considered, and it is shown that the theory of Wiener–Itô integrals provides a valuable tool in their study. …”
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“…This work starts with the study of those limit theorems in probability theory for which classical methods do not work. …”
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“…This book is intended for an audience with a graduate background in probability theory and statistics. It will be useful to any reader wondering why it may be a good idea, to use as is often done in practice a notoriously "wrong'' (i.e. over-simplified) model to predict, estimate or classify. …”
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“…A careful review of the prerequisites (integration and probability theory in the appendix, Hilbert spaces in the first chapter) make the book self-contained. …”
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