|
Books > Science & Mathematics > Mathematics
|
Buy Now
Young Measures on Topological Spaces - With Applications in Control Theory and Probability Theory (Hardcover, 2004 ed.)
Loot Price: R1,764
Discovery Miles 17 640
|
|
|
Young Measures on Topological Spaces - With Applications in Control Theory and Probability Theory (Hardcover, 2004 ed.)
Series: Mathematics and Its Applications, 571
Expected to ship within 10 - 15 working days
|
Donate to Gift Of The Givers
Total price: R1,784
Discovery Miles: 17 840
|
Classicalexamples of moreand more oscillatingreal-valued functions
on a domain N ?of R are the functions u (x)=sin(nx)with x=(x ,...,x
) or the so-called n 1 1 n n+1 Rademacherfunctionson]0,1[,u (x)=r
(x) = sgn(sin(2 ?x))(seelater3.1.4). n n They may appear as the
gradients?v of minimizing sequences (v ) in some n n n?N
variationalproblems. Intheseexamples,thefunctionu
convergesinsomesenseto n ameasure on ? xR, called Young measure. In
Functional Analysis formulation, this is the narrow convergence to
of the image of the Lebesgue measure on ? by ? ? (?,u (?)). In the
disintegrated form ( ) ,the parametrized measure n ? ??? ? captures
the possible scattering of the u around ?. n Curiously if (X ) is a
sequence of random variables deriving from indep- n n?N dent ones,
the n-th one may appear more and more far from the k ?rst ones as 2
if it was oscillating (think of orthonormal vectors in L which
converge weakly to 0). More precisely when the laws L(X ) narrowly
converge to some probability n measure , it often happens that for
any k and any A in the algebra generated by X ,...,X , the
conditional law L(X|A) still converges to (see Chapter 9) 1 k n
which means 1 ??? C (R) ?(X (?))dP(?)?? ?d b n P(A) A R or
equivalently, ? denoting the image of P by ? ? (?,X (?)), n X n (1l
??)d? ?? (1l ??)d[P? ].
General
Is the information for this product incomplete, wrong or inappropriate?
Let us know about it.
Does this product have an incorrect or missing image?
Send us a new image.
Is this product missing categories?
Add more categories.
Review This Product
No reviews yet - be the first to create one!
|
You might also like..
|
Welcome to Loot.co.za!
Sign in / Register |Wishlists & Gift Vouchers |Help | Advanced search
(1)
