Young Measures on Topological Spaces

With Applications in Control Theory and Probability Theory

Charles Castaing, Paul Raynaud de Fitte, Michel Valadier (Autoren)

Buch | Softcover

320 Seiten

2010 | Softcover reprint of the original 1st ed. 2004
Springer (Verlag)
978-90-481-6552-0 (ISBN)

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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? ].

Generalities, preliminary results.- Young measures, the four stable topologies: S, M, N, W.- Convergence in probability of Young measures (with some applications to stable convergence).- Compactness.- Strong tightness.- Young measures on Banach spaces. Applications.- Applications in Control Theory.- Semicontinuity of integral functionals using Young measures.- Stable convergence in limit theorems of probability theory.

Erscheint lt. Verlag	4.12.2010
Reihe/Serie	Mathematics and Its Applications ; 571
Zusatzinfo	XII, 320 p.
Verlagsort	Dordrecht
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik
	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	90-481-6552-0 / 9048165520
ISBN-13	978-90-481-6552-0 / 9789048165520
Zustand	Neuware