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Multifractional stochastic fields = ...

Ayache, Antoine.

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Multifractional stochastic fields = wavelet strategies in multifractional frameworks /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Multifractional stochastic fields/ Antoine Ayache.
其他題名:	wavelet strategies in multifractional frameworks /
作者:	Ayache, Antoine.
出版者:	Singapore :World Scientific, : c2019.,
面頁冊數:	1 online resource (235 p.) :ill. (some col.)
標題:	Brownian motion processes. -
電子資源:	https://www.worldscientific.com/worldscibooks/10.1142/8917#t=toc
ISBN:	9789814525664

Multifractional stochastic fields = wavelet strategies in multifractional frameworks /
Ayache, Antoine.

Multifractional stochastic fieldswavelet strategies in multifractional frameworks /[electronic resource] :Antoine Ayache. - 1st ed. - Singapore :World Scientific,c2019. - 1 online resource (235 p.) :ill. (some col.)

Includes bibliographical references.

"Fractional Brownian Motion (FBM) is a very classical continuous self-similar Gaussian field with stationary increments. In 1940, some works of Kolmogorov on turbulence led him to introduce this quite natural extension of Brownian Motion, which, in contrast with the latter, has correlated increments. However, the denomination FBM is due to a very famous article by Mandelbrot and Van Ness, published in 1968. Not only in it, but also in several of his following works, Mandelbrot emphasized the importance of FBM as a model in several applied areas, and thus he made it to be known by a wide community. Therefore, FBM has been studied by many authors, and used in a lot of applications. In spite of the fact that FBM is a very useful model, it does not always fit to real data. This is the reason why, for at least two decades, there has been an increasing interest in the construction of new classes of random models extending it, which offer more flexibility. A paradigmatic example of them is the class of Multifractional Fields. Multifractional means that fractal properties of models, typically, roughness of paths and self-similarity of probability distributions, are locally allowed to change from place to place. In order to sharply determine path behavior of Multifractional Fields, a wavelet strategy, which can be considered to be new in the probabilistic framework, has been developed since the end of the 90's. It is somehow inspired by some rather non-standard methods, related to the fine study of Brownian Motion roughness, through its representation in the Faber–Schauder system. The main goal of the book is to present the motivations behind this wavelet strategy, and to explain how it can be applied to some classical examples of Multifractional Fields. The book also discusses some topics concerning them which are not directly related to the wavelet strategy."--

Electronic reproduction.
Singapore :
World Scientific,
[2018]

Mode of access: World Wide Web.

ISBN: 9789814525664Subjects--Topical Terms:

646794
Brownian motion processes.

LC Class. No.: QA274.75 / .A93 2019

Dewey Class. No.: 519.2/3

Multifractional stochastic fields = wavelet strategies in multifractional frameworks /
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520 $a "Fractional Brownian Motion (FBM) is a very classical continuous self-similar Gaussian field with stationary increments. In 1940, some works of Kolmogorov on turbulence led him to introduce this quite natural extension of Brownian Motion, which, in contrast with the latter, has correlated increments. However, the denomination FBM is due to a very famous article by Mandelbrot and Van Ness, published in 1968. Not only in it, but also in several of his following works, Mandelbrot emphasized the importance of FBM as a model in several applied areas, and thus he made it to be known by a wide community. Therefore, FBM has been studied by many authors, and used in a lot of applications. In spite of the fact that FBM is a very useful model, it does not always fit to real data. This is the reason why, for at least two decades, there has been an increasing interest in the construction of new classes of random models extending it, which offer more flexibility. A paradigmatic example of them is the class of Multifractional Fields. Multifractional means that fractal properties of models, typically, roughness of paths and self-similarity of probability distributions, are locally allowed to change from place to place. In order to sharply determine path behavior of Multifractional Fields, a wavelet strategy, which can be considered to be new in the probabilistic framework, has been developed since the end of the 90's. It is somehow inspired by some rather non-standard methods, related to the fine study of Brownian Motion roughness, through its representation in the Faber–Schauder system. The main goal of the book is to present the motivations behind this wavelet strategy, and to explain how it can be applied to some classical examples of Multifractional Fields. The book also discusses some topics concerning them which are not directly related to the wavelet strategy."-- $c Publisher's website.
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