| Derivation and Martingales Softcover Repri Edition Contributor(s): Hayes, Charles A. (Author), Pauc, C. y. (Author) |
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ISBN: 3642861822 ISBN-13: 9783642861826 Publisher: Springer OUR PRICE: $52.24 Product Type: Paperback - Other Formats Published: April 2012 |
| Additional Information |
| BISAC Categories: - Gardening - Mathematics | Probability & Statistics - General |
| Dewey: 519.2 |
| Series: Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 2. Folge |
| Physical Information: 0.46" H x 6.14" W x 9.21" (0.68 lbs) 206 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |