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Titlebook: Stochastic Partial Differential Equations; Sergey V. Lototsky,Boris L. Rozovsky Textbook 2017 Springer International Publishing AG 2017 60

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发表于 2025-3-21 18:14:30 | 显示全部楼层 |阅读模式
书目名称Stochastic Partial Differential Equations
编辑Sergey V. Lototsky,Boris L. Rozovsky
视频video
概述Covers material for about 40 hours of lectures for everybody working in the area of stochastic analysis, from beginning graduate students to experts in the field.Presents exercise material to fill pot
丛书名称Universitext
图书封面Titlebook: Stochastic Partial Differential Equations;  Sergey V. Lototsky,Boris L. Rozovsky Textbook 2017 Springer International Publishing AG 2017 60
描述.Taking readers with a basic knowledge of probability and real analysis to the frontiers of a very active research discipline, this textbook provides all the necessary background from functional analysis and the theory of PDEs. It covers the main types of equations (elliptic, hyperbolic and parabolic) and discusses different types of random forcing. The objective is to give the reader the necessary tools to understand the proofs of existing theorems about SPDEs (from other sources) and perhaps even to formulate and prove a few new ones. Most of the material could be covered in about 40 hours of lectures, as long as not too much time is spent on the general discussion of stochastic analysis in infinite dimensions... As the subject of SPDEs is currently making the transition from the research level to that of a graduate or even undergraduate course, the book attempts to present enough exercise material to fill potential exams and homework assignments. Exercises appear throughout and are usually directly connected to the material discussed at a particular place in the text. The questions usually ask to verify something, so that the reader already knows the answer and, if pressed for t
出版日期Textbook 2017
关键词60H15, 35R60; stochastic parabolic equations; stochastic hyperbolic equations; stochastic elliptic equa
版次1
doihttps://doi.org/10.1007/978-3-319-58647-2
isbn_softcover978-3-319-58645-8
isbn_ebook978-3-319-58647-2Series ISSN 0172-5939 Series E-ISSN 2191-6675
issn_series 0172-5939
copyrightSpringer International Publishing AG 2017
The information of publication is updating

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发表于 2025-3-21 20:16:26 | 显示全部楼层
Textbook 2017all the necessary background from functional analysis and the theory of PDEs. It covers the main types of equations (elliptic, hyperbolic and parabolic) and discusses different types of random forcing. The objective is to give the reader the necessary tools to understand the proofs of existing theor
发表于 2025-3-22 00:53:47 | 显示全部楼层
0172-5939 experts in the field.Presents exercise material to fill pot.Taking readers with a basic knowledge of probability and real analysis to the frontiers of a very active research discipline, this textbook provides all the necessary background from functional analysis and the theory of PDEs. It covers th
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发表于 2025-3-22 08:46:12 | 显示全部楼层
The Polynomial Chaos Method,ion of this idea for stochastic equations. While the elementary outcome . is typically never mentioned explicitly in the notation of random objects, it is a variable that can potentially be separated from other variables, and the objective of this chapter is to outline a systematic approach to doing
发表于 2025-3-22 14:22:05 | 显示全部楼层
Basic Ideas,responds to .; a . corresponds to ., .. A ., or . of . is the function .(⋅ , .) for fixed . ∈ .. A . of . is a random function . such that, for every . ∈ ., .; note that this, in general, DOES NOT mean that . (although it does if both . and . are continuous).
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Universitexthttp://image.papertrans.cn/s/image/878075.jpg
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发表于 2025-3-23 04:12:27 | 显示全部楼层
Introduction,We use the same notation . for a point in the real line . or in a d-dimensional Euclidean space ..For ., .; for ., . = .... + . + ..... Integral over the real line can be written either as . or as .... Sometimes, when there is no danger of confusion, the domain of integration, in any number of dimensions, is omitted altogether.
发表于 2025-3-23 06:39:49 | 显示全部楼层
Stochastic Analysis in Infinite Dimensions,This chapter contains somewhat abstract but necessary, material on functional analysis and stochastic calculus. To save time, one can move on to the following chapters and come back as necessary.
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