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Stochastic Equations for Complex Systems
The purpose of these notes is to provide an introduction to the Malliavin calculus and its recent application to quantitative results in normal approximations, in combination with Stein’s method. The basic differential operators of the Malliavin calculus and their main properties are presented. We explain the connection of these operators with the Wiener chaos expansion and the Ornstein-Uh…
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- 978-3-319-18206-3
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Stochastic Dynamics of Crystal Defects
The state of a deformed crystal is highly heterogeneous, with plasticity localised into linear and point defects such as dislocations, vacancies and interstitial clusters. The motion of these defects dictate a crystal’s mechanical behaviour, but defect dynamics are complicated and correlated by external applied stresses, internal elastic interactions and the fundamentally stochastic influ…
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- 978-3-319-20019-4
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Stochastic Dynamics and Irreversibility
Erratic or irregular movements, which we call unpredictable or random, occur spontaneously and are essential part of microscopic and macroscopic worlds. When superimposed to the predictable movements, they make up the random fluctuations sometimes called noise. Heat and temperature are macroscopic manifestations of these fluctuations at the microscopic level, and statistical physics constit…
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- 978-3-319-11770-6
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Stochastic Dominance
Concepts similar to stochastic dominance have been known for many years, but the three papers published by Hadar and Russell and Hanoch and Levy in 1969 and by Rothschild and Stiglitz in 19701 paved the way for a new paradigm called stochastic dominance (SD), with hundreds of studies following these three studies. While Hanoch and Levy and Hadar and Russell developed First and Second degree…
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- 978-3-319-21708-6
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Stochastic Control Theory
The purpose of this book is to provide an introduction to stochastic controls theory, via the method of dynamic programming. The dynamic programming principle, originated by R. Bellman in 1950s, is known as the two stage optimization procedure. When we control the behavior of a stochastic dynamical system in order to optimize some payoff or cost function, which depends on the control inputs…
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- 978-4-431-55123-2
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Stochastic Calculus and Applications
The theory of probability and stochastic calculus has grown significantly since the publication of the first edition of this book. The theory of stochastic integration and semimartingales, a relatively recent development at the time of the first edition, is now a standard and significant part of the working mathematician’s toolkit. Concepts such as Backward SDEs, which were unheard of in 1…
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- 978-1-4939-2867-5
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Theory of Transformation Groups I
This modern translation of Sophus Lie's and Friedrich Engel's “Theorie der Transformationsgruppen I” will allow readers to discover the striking conceptual clarity and remarkably systematic organizational thought of the original German text. Volume I presents a comprehensive introduction to the theory and is mainly directed towards the generalization of ideas drawn from the study of example…
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- 978-3-662-46211-9
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- 7 illustrations in colour
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Theory of Heavy-Fermion Compounds
This book explains modern and interesting physics in heavy-fermion (HF) compounds to graduate students and researchers in condensed matter physics. It presents a theory of heavy-fermion (HF) compounds such as HF metals, quantum spin liquids, quasicrystals and two-dimensional Fermi systems. The basic low-temperature properties and the scaling behavior of the compounds are described within the fr…
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- ISBN/ISSN
- 978-3-319-10825-4
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- 117 b/w illustrations, 23 illustrations in colour
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Theory of Gas Discharge Plasma
This book presents the theory of gas discharge plasmas in a didactical way. It explains the processes in gas discharge plasmas. A gas discharge plasma is an ionized gas which is supported by an external electric field. Therefore its parameters are determined by processes in it. The properties of a gas discharge plasma depend on its gas component, types of external fields, their geometry and reg…
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- 978-3-319-11065-3
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- 196 b/w illustrations
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Non-perturbative Description of Quantum Systems
This book introduces systematically the operator method for the solution of the Schrödinger equation. This method permits to describe the states of quantum systems in the entire range of parameters of Hamiltonian with a predefined accuracy. The operator method is unique compared with other non-perturbative methods due to its ability to deliver in zeroth approximation the uniformly suitable est…
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- 1
- ISBN/ISSN
- 978-3-319-13006-4
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- XV, 362
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- Lecture Notes in Physics
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