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Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations
In this second volume, a general approach is developed to provide approximate parameterizations of the "small" scales by the "large" ones for a broad class of stochastic partial differential equations (SPDEs). This is accomplished via the concept of parameterizing manifolds (PMs), which are stochastic manifolds that improve, for a given realization of the noise, in mean square error the partial…
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- 978-3-319-12520-6
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Stochastic Optimization Methods
This book examines optimization problems that in practice involve random model parameters. It details the computation of robust optimal solutions, i.e., optimal solutions that are insensitive with respect to random parameter variations, where appropriate deterministic substitute problems are needed. Based on the probability distribution of the random data and using decision theoretical concepts…
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- 978-3-662-46214-0
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Stochastic Narrow Escape in Molecular and Cellular Biology
This book covers recent developments in the non-standard asymptotics of the mathematical narrow escape problem in stochastic theory, as well as applications of the narrow escape problem in cell biology. The first part of the book concentrates on mathematical methods, including advanced asymptotic methods in partial equations, and is aimed primarily at applied mathematicians and theoretical phys…
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- 978-1-4939-3103-3
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Stochastic Multi-Stage Optimization
The focus of the present volume is stochastic optimization of dynamical systems in discrete time where - by concentrating on the role of information regarding optimization problems - it discusses the related discretization issues. There is a growing need to tackle uncertainty in applications of optimization. For example the massive introduction of renewable energies in power systems challenges …
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- 978-3-319-18138-7
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Stochastic Models, Statistics and Their Applications
This volume presents papers collected on the occasion of the 12th Workshop on Stochastic Models, Statistics and Their Applications, jointly organized by the Institute of Mathematics and Computer Science of Wrocław University of Technology, the Institute of Computer Engineering, Control and Robotics, Wrocław University of Technology, and by the Institute of Statistics of RWTH Aachen Univers…
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- 978-3-319-13881-7
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Stochastic Models with Power-Law Tails
The Stochastic Equation. The authors of this text (called DB, ED and TM) started their collaboration with the paper Buraczewski et al. [76] in 2011. We studied large deviations and ruin probabilities for the solution ðXtÞ to Kesten’s stochastic recurrence equation
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- 978-3-319-29679-1
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Stochastic Models for Structured Populations
This course concerns the stochastic modeling of population dynamics. In the first part, we focus on monotype populations described by one-dimensional stochastic differential equations with jumps. We consider their scaling limits for large populations and study the long time behavior of the limiting processes. It is achieved, thanks to martingale properties, Poisson measure representations, a…
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- 978-3-319-21711-6
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Stochastic Modeling of Thermal Fatigue Crack Growth
The assessment of thermal fatigue crack growth due to turbulent mixing of hot and cold coolants presents significant challenges, in particular, to determine the thermal loading spectrum. Thermal striping is defined as a random temperature fluctuation produced by incomplete mixing of fluid streams at different temperatures, and it is essentially a random phenomenon in a temporal sense.
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- ISBN 978-3-319-12877-1
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Stochastic Integration in Banach Spaces
The study of stochastic differential equations (SDEs) driven by Lévy processes in R originated in the book by Skorokhod [97]. In view of the Lévy–Itô decomposition, he reduced the problem of studying such SDEs to the analysis of SDEs driven by compensated Poisson random measures (cPrms) and Brownian motion, under a mild restriction [97]. He was aware of the fact that the restriction ca…
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- 978-3-319-12853-5
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Nonlinear Mechanics of Soft Fibrous Materials
The book presents a state-of-the-art overview of the fundamental theories, established models and ongoing research related to the modeling of these materials. Two approaches are conventionally used to develop constitutive relations for highly deformable fibrous materials. According to the phenomenological approach, a strain energy density function can be defined in terms of strain invariants. T…
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- 1
- ISBN/ISSN
- 0254-1971
- Collation
- VII, 305
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- CISM International Centre for Mechanical Sciences
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