Download PDF by Ghora J.K.: A Central Limit Theorem for the L2 Error of Positive Wavelet

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Additional info for A Central Limit Theorem for the L2 Error of Positive Wavelet Density Estimator

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1 Linear equations Consider the problem on tracer transfer by random velocity field in more details. The problem is formulated in terms of Eq. 39), page 19 that we rewrite in the form | + U ( r , t ) ^ ) p ( r , f ) + ^ ^ ^ p ( r , « ) = 0, p{v,Q) = p,{v). 2) and is locahzed on surface p(r, t) = p = const in the three-dimensional case or on a contour in the two-dimensional case. An equation for this function can be easily obtained either immediately from Eq. 5), or from the Liouville equation in the Lagrangian description.

Chapter 3. 1: To the definition of the typical realization curve of a random process. R a n d o m processes Following works [143, 166], we discuss first the concept of typical realization curve of r a n d o m process z{t). This concept concerns t h e fundamental features of the behavior of a separate process realization as a whole for temporal intervals of arbitrary duration. 27) = 1/2. T h e reason to this definition rests on the median property consisting in the fact t h a t , for any temporal interval (ti,/;2)?

According to the material of the previous section, realizations of intensity must show the cluster behavior, which manifests itself in the appearance of caustic structures. An example demonstrating the appearance of the wavefield caustic structures is given in Fig. 11, which is a fragment of the photo on the back of the cover — the flyleaf - of book [268) t h a t shows the transverse section of the laser b e a m propagating in the turbulent atmosphere (see also papers [64, 65, 103] for the results of laboratory investigations and simulations).

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A Central Limit Theorem for the L2 Error of Positive Wavelet Density Estimator by Ghora J.K.


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