Continuous Mapping Theorem : Probability Theory, Continuous Function, Convergence of Random Variables, Portmanteau Theorem, Closure (topology).

Frederic P. Miller

ISBN 10: 6133791136 / ISBN 13: 9786133791138

Published by Omniscriptum, 2010

About this Item

nach der Bestellung gedruckt Neuware - Printed after ordering.

Seller Inventory # 9786133791138

Bibliographic Details

• Title: Continuous Mapping Theorem : Probability Theory, Continuous Function, Convergence of Random Variables, Portmanteau Theorem, Closure (topology).
• Publisher: Omniscriptum
• Publication Date: 2010
• Language: English
• ISBN 10: 6133791136
• ISBN 13: 9786133791138
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 220W x 150H x 4D millimeters 220 millimeters width by 150 millimeters height by 4 millimeters depth
• Weight: 113 grams

About this title

Synopsis

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In probability theory, the continuous mapping theorem states that continuous functions are limit- preserving even if their arguments are sequences of random variables. A continuous function, in Heine’s definition, is such a function that maps convergent sequences into convergent sequences: if xn → x then g (xn) → g(x). The continuous mapping theorem states that this will also be true if we replace the deterministic sequence {xn} with a sequence of random variables {Xn}, and replace the standard notion of convergence of real numbers “→� with one of the types of convergence of random variables.