Download e-book for kindle: Entscheidungsregeln bei Risiko Multivariate stochastische by Priv.-Doz. Dr. K. C. Mosler (auth.)

By Priv.-Doz. Dr. K. C. Mosler (auth.)

ISBN-10: 3540119442

ISBN-13: 9783540119449

ISBN-10: 3642954197

ISBN-13: 9783642954191

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Extra info for Entscheidungsregeln bei Risiko Multivariate stochastische Dominanz

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3. Kamae, Krengel und O'Brien(1977 und 1978) haben gezeigt, daB unter diesen Voraussetzungen~u eine antisymmetrische und abgeschlossene 1 1 Relation in M+ ist. 4 Satz: Sei E ein halbgeordneter polnischer Raum; fur 1 A,)lEM+ sind die folgenden Aussagen aquivalent: (i) A ~Ul)l (i i) Es gi bt einen Markoff-Kern 1) K, so daB )l (A) f K(x,A) A(dx) fur alle A ES und K(x,R ) x E = 1 fur alle xEE. (iii) Es gibt Zufallsvariable X,V und Z in E, so daB fast sicher X = V + Z und Z~O gilt, und X die Verteilung A, V die Verteilung )l besitzt.

T~iheh, also eine Hatbo~dnung in Mist. Zu- nachst ist grob zu vermuten, daB Antisyrnmetrie vorliegt, wenn U reichhaltig genug ist und/oder wenn M nicht zuviele Elemente umfaBt. Zum Beispiel sei E = 1R und U die Menge, die nur die identische Abbildung enthalt,und seien X und Y reelle Zufallsvariable. Man erhalt X ~U Y .... EX ~ EY, das sogenannte Erwartungswertkri- 38 terium. ~U lSBt sich "antisymmetrisch machen", indem man es auf Zufallsvariable aus einer parametrischen Verteilungsklasse M einschrSnkt (mit dem Erwartungswert als Parameter).

Ht de r en Umke h run 9 . h. von jedem Ausgangspunkt x mit Wahrscheinlichkeit 1 zu Punkten grHBer oder gleich x fUhrt. Eine Relation. die ebenfalls bereits unter sehr allgemeinen Annahmen untersucht worden ist, ist die stochastische Dominanz bezUglich der Klasse Ue aller konkaven Funktionen, Uc = rUE B(E)\ u konkav}. Wenn E eine konvexe und (J"-kompakte Teilmenge eines lokalkonvexen topologischen Vektorraums ist, laBt sich zeigen 1 ), daB ~ U eine antisymmetrische Relation in c M~ ist. 4 ahnlicher Satz.

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Entscheidungsregeln bei Risiko Multivariate stochastische Dominanz by Priv.-Doz. Dr. K. C. Mosler (auth.)

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