Shortcuts
Top of page (Alt+0)
Page content (Alt+9)
Page menu (Alt+8)
Your browser does not support javascript, some WebOpac functionallity will not be available.
.
Default
.
PageMenu
-
Main Menu
-
Simple Search
.
Advanced Search
.
Journal Search
.
Refine Search Results
.
Preferences
.
Search Menu
Simple Search
.
Advanced Search
.
New Items Search
.
Journal Search
.
Refine Search Results
.
Bottom Menu
Help
Italian
.
English
.
German
.
New Item Menu
New Items Search
.
New Items List
.
Links
SISSA Library
.
ICTP library
.
Italian National web catalog (SBN)
.
Trieste University web catalog
.
Udine University web catalog
.
© LIBERO v6.4.1sp220816
Page content
You are here
:
Catalogue Tag Display
Catalogue Tag Display
MARC 21
Derivation and Martingales
Tag
Description
020
$a9783642861802$9978-3-642-86180-2
082
$a519.2$223
099
$aOnline resource: Springer
100
$aHayes, Charles A.
245
$aDerivation and Martingales$h[EBook] /$cby Charles A. Hayes, Christian Y. Pauc.
260
$aBerlin, Heidelberg :$bSpringer Berlin Heidelberg,$c1970.
300
$aVIII, 206 p. 1 illus.$bonline resource.
336
$atext$btxt$2rdacontent
337
$acomputer$bc$2rdamedia
338
$aonline resource$bcr$2rdacarrier
440
$aErgebnisse der Mathematik und ihrer Grenzgebiete,$x0071-1136 ;$v49
505
$a
I Pointwise Derivation -- I: Derivation Bases -- II: Derivation Theorems for ?-additive Set Functions under Assumptions of the Vitali Type -- III: The Converse Problem I: Covering Properties Deduced from Derivation Properties of ?-additive Set Functions -- IV: Halo Assumptions in Derivation Theory. Converse Problem II -- V: The Interval Basis. The Theorem of Jessen-Marcin-Kiewicz-Zygmund -- VI: A. P. Morse’s Blankets -- II Martingales and Cell Functions -- I: Theory without an Intervening Measure -- II: Theory in a Measure Space without Vitali Conditions -- III: Theory in a Measure Space with Vitali Conditions -- IV: Applications -- Complements -- 1°. Derivation of vector-valued integrals -- 2°. Functional derivatives -- 3°. Topologies generated by measures -- 4°. Vitali’s theorem for invariant measures -- 5°. Global derivatives in locally compact topological groups. -- 6°. Submartingales with decreasing stochastic bases -- 7°. Vector-valued martingales and derivation -- 9°. Derivation of measures.
520
$a
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.
538
$aOnline access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
700
$aPauc, Christian Y.$eauthor.
710
$aSpringerLink (Online service)
830
$aErgebnisse der Mathematik und ihrer Grenzgebiete,$x0071-1136 ;$v49
856
$u
http://dx.doi.org/10.1007/978-3-642-86180-2
Quick Search
Search for