...ditions, [[#References|[a3]]], M-estimators are asymptotically normal with asymptotic variance $V ( T , F _ { \theta } ) = \int \operatorname { IF } ( x ; T , F
...Huber's minimax variance problem [[#References|[a1]]] or by minimizing the asymptotic variance $V ( T , F _ { \theta } )$ subject to an upper bound on the gross-
13 KB (1,756 words) - 17:42, 1 July 2020
...op">[3]</TD> <TD valign="top"> I.S. Ibragimov, "Statistical estimation: asymptotic theory" , Springer (1981) (Translated from Russian)</TD></TR></table>
3 KB (375 words) - 16:43, 20 January 2022
...The Mikhailov criterion gives a necessary and sufficient condition for the asymptotic stability of a linear differential equation of order $n$,
...op">[a2]</td> <td valign="top"> B.R. Barmish, "New tools for robustness analysis" , ''IEEE Proc. 27th Conf. Decision and Control, Austin, Texas, December 19
5 KB (692 words) - 15:30, 1 July 2020
asymptotic approximation of the function:
...valign="top">[2]</TD> <TD valign="top"> L.D. Kudryavtsev, "Mathematical analysis" , Moscow (1973) (In Russian)</TD></TR></table>
3 KB (410 words) - 18:48, 5 April 2020
...e the flame. The complete profiles are then found by the method of matched asymptotic expansions (cf. [[Perturbation theory|Perturbation theory]]).
...top">[a2]</TD> <TD valign="top"> W.B. Bush, F.E. Fendell, "Asymptotic analysis of laminar flame propagation for general Lewis numbers" ''Comb. Sci. and T
5 KB (707 words) - 16:08, 1 April 2020
...or of the]]) can be obtained by some further constructions that employ the asymptotic lack of correlation for the periodograms for different frequencies $ \lam
...gn="top">[1]</TD> <TD valign="top"> D.R. Brillinger, "Time series. Data analysis and theory" , Holt, Rinehart & Winston (1974)</TD></TR><TR><TD valign=
3 KB (404 words) - 08:57, 25 April 2022
...based on a combination of time-dependent scattering theory and phase-space analysis. In his first work, Enss solved the two-body scattering problem (with short
...ficial assumptions. It also initiated the fruitful approach of phase-space analysis, later further developed by E. Mourre [[#References|[a3]]] (1979–1981) an
9 KB (1,396 words) - 16:57, 1 July 2020
the asymptotic normality of the variable $ Z _ {n} = \sqrt n ( X _ {n} - x _ {0} ) $
...res possess properties that are asymptotically optimal in the sense of the asymptotic variance.
9 KB (1,349 words) - 08:23, 6 June 2020
...otics of Toeplitz determinants can be used to obtain information about the asymptotic distribution of the eigenvalues $\{ \lambda _ { k } ^ { ( n ) } \} _ { k =
...number|winding number]] of the function $a ( e ^ { i \theta } ) - z$. The asymptotic formula (a3) is sometimes also called the first Szegö limit theorem or a f
13 KB (1,838 words) - 07:22, 13 February 2024
...ectrum of $T$, and provide a powerful tool of [[Spectral analysis|spectral analysis]].
In order to carry out a more detailed spectral analysis of the Sturm–Liouville operator $T$, one has to consider the spectral mea
23 KB (3,372 words) - 17:44, 1 July 2020
...ese problems have many applications in mathematical statistics (sequential analysis), in the insurance business, in queueing theory, etc. In their investigatio
...walks have been investigated rather completely, including their asymptotic analysis (see [[#References|[1]]], Vol. 2; [[#References|[4]]]–).
18 KB (2,649 words) - 20:12, 12 January 2024
...he Picard exceptional values are asymptotic values (cf. [[Asymptotic value|Asymptotic value]]) and that there exist Julia rays $ L $
...="top">[3]</TD> <TD valign="top"> B.V. Shabat, "Introduction of complex analysis" , '''1–2''' , Moscow (1976) (In Russian)</TD></TR><TR><TD valign="top"
8 KB (1,225 words) - 08:06, 6 June 2020
...to give, under the assumptions $\int_\cK Vdx = 0$ and $n\ge 2$, a precise asymptotic formula, as $\mu\to +\infty$, for $N(\mu)$ in the following form:
|valign="top"|{{Ref|HeMo}}||valign="top"| B. Helffer, A. Mohamed, "Asymptotic of the density of states for the Schrödinger operator with periodic electr
8 KB (1,239 words) - 16:33, 4 December 2017
...only on the boundary of $g$, but also everywhere inside. The procedure of asymptotic integration used in shell theory for non-regular degeneration has not yet (
...of the corresponding forms of free vibration have been found by methods of asymptotic integration and by the spectral theory of operators (see [[#References|[5]]
8 KB (1,200 words) - 17:04, 14 February 2020
...necessary characteristics, or is in some sense critical. The direction of asymptotic investigation in the first case is described by stability (or continuity) t
...TD></TR><TR><TD valign="top">[4]</TD> <TD valign="top"> A.A. Borovkov, "Asymptotic methods in queueing theory" , Wiley (1984) (Translated from Russian)</TD>
12 KB (1,824 words) - 08:09, 6 June 2020
...ccurring in the area of statistics called [[Sequential analysis|sequential analysis]]. In sequential procedures for statistical estimation, hypothesis testing
...then follows from (a3) and agrees with (a2). See [[#References|[a1]]] for asymptotic properties of the average sample number for curtailed tests in general.
8 KB (1,155 words) - 19:33, 2 February 2024
An asymptotic approximation of the solution of boundary value problems for differential e
...nstructed for a particular type of integro-differential equation giving an asymptotic expansion in $ \epsilon $
24 KB (3,570 words) - 08:40, 26 March 2023
...l equations with deviated arguments includes all equations of mathematical analysis. Nevertheless, ordinary differential equations with deviated arguments are
is necessary and sufficient for the asymptotic stability of solutions of equation (5). If this condition is met, the zero
27 KB (3,819 words) - 16:54, 7 February 2011
that is, to construct an asymptotic solution as $ \epsilon \rightarrow 0 $,
denotes asymptotic equality. All vector and matrix functions which appear in equations and bou
35 KB (4,975 words) - 14:55, 7 June 2020
...al of such a function. Operators of this type arose when investigating the asymptotic expansions of rapidly-oscillating solutions to partial differential equatio
is a formal asymptotic solution of the equation $ L ( x, \lambda ^ {-} 1 D) u = 0 $.
24 KB (3,360 words) - 19:39, 5 June 2020