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Derivation and Martingales by Charles A. Hayes, C.Y. Pauc (Paperback, 2012)

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In Part I of this report the pointwise derivation of scalar set functions is investigated, first along the lines of R. DE POSSEL (abstract derivation basis) and A. P. MORSE (blankets); later certain concrete situations (e. g. , the interval basis) are studied. The principal tool is a Vitali property, whose precise form depends on the derivation property studied. The halo (defined at the beginning of Part I, Ch. IV) properties can serve to establish a Vitali property, or sometimes produce directly a derivation property. The main results established are the theorem of JESSEN-MARCINKIEWICZ-ZYGMUND (Part I, Ch. V) and the theorem of A. P. MORSE on the universal derivability of star blankets (Ch. VI) . . In Part II, points are at first discarded; the setting is somatic. It opens by treating an increasing stochastic basis with directed index sets (Th. I. 3) on which premartingales, semimartingales and martingales are defined. Convergence theorems, due largely to K. KRICKEBERG, are obtained using various types of convergence: stochastic, in the mean, in Lp-spaces, in ORLICZ spaces, and according to the order relation. We may mention in particular Th. II. 4. 7 on the stochastic convergence of a submartingale of bounded variation. To each theorem for martingales and semi-martingales there corresponds a theorem in the atomic case in the theory of cell (abstract interval) functions. The derivates concerned are global. Finally, in Ch.

Product Identifiers

Publisher
Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
ISBN-13
9783642861826
eBay Product ID (ePID)
190321506

Product Key Features

Author
Charles A. Hayes, C.Y. Pauc
Publication Name
Derivation and Martingales
Format
Paperback
Language
English
Subject
Mathematics
Publication Year
2012
Type
Textbook
Number of Pages
206 Pages

Dimensions

Item Height
235mm
Item Width
155mm
Volume
49
Item Weight
338g

Additional Product Features

Title_Author
C.Y. Pauc, Charles A. Hayes
Series Title
Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 2. Folge
Country/Region of Manufacture
Germany

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