ISBN: 9789048165520

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… Meer...

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 µ on ? ×R, called Young measure. In Functional Analysis formulation, this is the narrow convergence to µ of the image of the Lebesgue measure on ? by ? ? (?,u (?)). In the disintegrated form (µ ) ,the parametrized measure µ 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? ]. Books > Science & Nature > Math & Physics > Mathematics List_Books<

ISBN: 9789048165520

Paperback, [PU: Springer], 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 … Meer...

Paperback, [PU: Springer], 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? ]., Integral Calculus & Equations<

2013, ISBN: 9789048165520

Springer, Taschenbuch, Auflage: Softcover reprint of the original 1st ed. 2004, 336 Seiten, Publiziert: 2013-10-04T00:00:01Z, Produktgruppe: Buch, 1.14 kg, Analysis, Naturwissenschaft & M… Meer...

Springer, Taschenbuch, Auflage: Softcover reprint of the original 1st ed. 2004, 336 Seiten, Publiziert: 2013-10-04T00:00:01Z, Produktgruppe: Buch, 1.14 kg, Analysis, Naturwissenschaft & Mathematik, Fachbücher, Kategorien, Bücher, Geometrie, Statistik, Naturwissenschaften & Technik, Springer, 2013<

2013, ISBN: 9789048165520

Springer, Taschenbuch, Auflage: Softcover reprint of the original 1st ed. 2004, 336 Seiten, Publiziert: 2013-10-04T00:00:01Z, Produktgruppe: Buch, 1.14 kg, Analysis, Naturwissenschaft & M… Meer...

Springer, Taschenbuch, Auflage: Softcover reprint of the original 1st ed. 2004, 336 Seiten, Publiziert: 2013-10-04T00:00:01Z, Produktgruppe: Buch, 1.14 kg, Analysis, Naturwissenschaft & Mathematik, Fachbücher, Kategorien, Bücher, Geometrie, Statistik, Naturwissenschaften & Technik, Springer, 2013<

2010, ISBN: 9789048165520

With Applications in Control Theory and Probability Theory, Buch, Softcover, Softcover reprint of the original 1st ed. 2004, [PU: Springer], Springer, 2010