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Titlebook: Stochastic Differential Equations; An Introduction with Bernt ?ksendal Textbook 19892nd edition Springer-Verlag Berlin Heidelberg 1989 Brow

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樓主
發(fā)表于 2025-3-21 17:16:54 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書目名稱Stochastic Differential Equations
副標(biāo)題An Introduction with
編輯Bernt ?ksendal
視頻videohttp://file.papertrans.cn/878/877900/877900.mp4
叢書名稱Universitext
圖書封面Titlebook: Stochastic Differential Equations; An Introduction with Bernt ?ksendal Textbook 19892nd edition Springer-Verlag Berlin Heidelberg 1989 Brow
描述.From the reviews: ."The author, a lucid mind with a fine pedagogical instinct, has written a splendid text. He starts out by stating six problems in the introduction in which stochastic differential equations play an essential role in the solution. Then, while developing stochastic calculus, he frequently returns to these problems and variants thereof and to many other problems to show how the theory works and to motivate the next step in the theoretical development. Needless to say, he restricts himself to stochastic integration with respect to Brownian motion. He is not hesitant to give some basic results without proof in order to leave room for "some more basic applications... The book can be an ideal text for a graduate course, but it is also recommended to analysts (in particular, those working in differential equations and deterministic dynamical systems and control) who wish to learn quickly what stochastic differential equations are all about." .Acta Scientiarum . .Mathematicarum, Tom 50, 3-4, 1986.#1 "The book is well written, gives a lot of nice applications of stochastic differential equation theory, and presents theory and applications of stochastic differential equati
出版日期Textbook 19892nd edition
關(guān)鍵詞Brownian motion; Differential Equations; Equations; Optimal Filtering; Stochastic Control; Stochastic cal
版次2
doihttps://doi.org/10.1007/978-3-662-02574-1
isbn_ebook978-3-662-02574-1Series ISSN 0172-5939 Series E-ISSN 2191-6675
issn_series 0172-5939
copyrightSpringer-Verlag Berlin Heidelberg 1989
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沙發(fā)
發(fā)表于 2025-3-21 22:51:20 | 只看該作者
板凳
發(fā)表于 2025-3-22 04:24:44 | 只看該作者
Diffusions: Basic Properties,he velocity of the fluid at the point x at time t, then a reasonable mathematical model for the position X. of the particle at time t would be a stochastic differential equation of the form . where W. ∈ ?. denotes “white noise” and .(t, x) ∈ ?.. The Ito interpretation of this equation is . where B.
地板
發(fā)表于 2025-3-22 05:06:57 | 只看該作者
Application to Stochastic Control,ownian motion. Here u ∈ R. is a parameter whose value we can choose at any instant in order to control the process X. · Thus u=u(t,ω) is a stochastic process. Since our decision at time t must be based upon what has happened up to time t, the function ω→u(t,ω) must (at least) be measurable wrt. ..,
5#
發(fā)表于 2025-3-22 09:21:34 | 只看該作者
Application to Stochastic Control,i.e. the process u. must be ..-adapted. Thus the right hand side of (11.1) is well-defined as a stochastic integral, under suitable assumptions on b and σ. At the moment we will not specify the conditions on b and a further, but simply assume that the process X. satisfying (11.1) exists. See further comments on this in the end of this chapter.
6#
發(fā)表于 2025-3-22 16:31:56 | 只看該作者
7#
發(fā)表于 2025-3-22 17:39:54 | 只看該作者
Springer-Verlag Berlin Heidelberg 1989
8#
發(fā)表于 2025-3-22 23:56:05 | 只看該作者
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Universitexthttp://image.papertrans.cn/s/image/877900.jpg
10#
發(fā)表于 2025-3-23 08:07:16 | 只看該作者
https://doi.org/10.1007/978-3-662-02574-1Brownian motion; Differential Equations; Equations; Optimal Filtering; Stochastic Control; Stochastic cal
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