Vector Integration and Stochastic Integration in Banach Spaces

Nicolae Dinculeanu (Autor)

Buch | Hardcover

474 Seiten

2000
Wiley-Interscience (Verlag)
978-0-471-37738-2 (ISBN)

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A breakthrough approach to the theory and applications of stochastic integration The theory of stochastic integration has become an intensely studied topic in recent years, owing to its extraordinarily successful application to financial mathematics, stochastic differential equations, and more. This book features a new measure theoretic approach to stochastic integration, opening up the field for researchers in measure and integration theory, functional analysis, probability theory, and stochastic processes. World-famous expert on vector and stochastic integration in Banach spaces Nicolae Dinculeanu compiles and consolidates information from disparate journal articles-including his own results-presenting a comprehensive, up-to-date treatment of the theory in two major parts. He first develops a general integration theory, discussing vector integration with respect to measures with finite semivariation, then applies the theory to stochastic integration in Banach spaces. Vector Integration and Stochastic Integration in Banach Spaces goes far beyond the typical treatment of the scalar case given in other books on the subject. Along with such applications of the vector integration as the Reisz representation theorem and the Stieltjes integral for functions of one or two variables with finite semivariation, it explores the emergence of new classes of summable processes that make applications possible, including square integrable martingales in Hilbert spaces and processes with integrable variation or integrable semivariation in Banach spaces. Numerous references to existing results supplement this exciting, breakthrough work.

Nicolae Dinculeanu is the author of Vector Integration and Stochastic Integration in Banach Spaces, published by Wiley.

Vector Integration.

The Stochastic Integral.

Martingales.

Processes with Finite Variation.

Processes with Finite Semivariation.

The Itô Formula.

Stochastic Integration in the Plane.

Two-Parameter Martingales.

Two-Parameter Processes with Finite Variation.

Two-Parameter Processes with Finite Semivariation.

References.

Erscheint lt. Verlag	15.2.2000
Reihe/Serie	Wiley Series in Pure and Applied Mathematics
Sprache	englisch
Maße	168 x 245 mm
Gewicht	758 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
ISBN-10	0-471-37738-4 / 0471377384
ISBN-13	978-0-471-37738-2 / 9780471377382
Zustand	Neuware