Random Series and Stochastic Integrals: Single and Multiple: Single and Multiple: Single and Multiple (Probability and Its Applications) - Softcover

Woyczynski, Wojbor A.; Kwapien, Stanislaw

Softcover

ISBN 10: 081764198X ISBN 13: 9780817641986

Verlag: Springer, 2008

Inhaltsangabe

This book studies the foundations of the theory of linear and nonlinear forms in single and multiple random variables including the single and multiple random series and stochastic integrals, both Gaussian and non-Gaussian. This subject is intimately connected with a number of classical problems of probability theory such as the summation of independent random variables, martingale theory, and Wiener's theory of polynomial chaos. The book contains a number of older results as well as more recent, or previously unpublished, results. The emphasis is on domination principles for comparison of different sequences of random variables and on decoupling techniques. These tools prove very useful in many areas ofprobability and analysis, and the book contains only their selected applications. On the other hand, the use of the Fourier transform - another classical, but limiting, tool in probability theory - has been practically eliminated. The book is addressed to researchers and graduate students in prob­ ability theory, stochastic processes and theoretical statistics, as well as in several areas oftheoretical physics and engineering. Although the ex­ position is conducted - as much as is possible - for random variables with values in general Banach spaces, we strive to avoid methods that would depend on the intricate geometric properties of normed spaces. As a result, it is possible to read the book in its entirety assuming that all the Banach spaces are simply finite dimensional Euclidean spaces.

Über diesen Titel

Reseña del editor

This volume studies the foundations of the theory of linear and nonlinear forms in single and multiple random variables including single and multiple random series and stochastic integrals, both Gaussian and non-Gaussian. Its topic is intimately connected with a number of classical problems of probability theory such as the summation of independent random variables, martingale theory and the Weiner theory of polynomial chaos, as well as with several application areas such as stochastic analysis, limit theorems for symmetric statistics, representation of random fields, partial differential equations and quantum field theory. The emphasis is on domination principles for comparison of sequences of random variables and on decoupling techniques. The volume is intended for researchers and graduate students in probability theory, stochastic processes, theoretical statistics and in several areas of theoretical physics and engineering.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2008
• Sprache: Englisch
• ISBN 10: 081764198X
• ISBN 13: 9780817641986
• Einband: Tapa blanda
• Anzahl der Seiten: 380
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Nicht verfügbar