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Functional Analysis for Probability and Stochastic Processes: An Introduction

✍ Scribed by Adam Bobrowski

Book ID
127426500
Publisher
Cambridge University Press
Year
2005
Tongue
English
Weight
2 MB
Category
Library
ISBN
0511130392

No coin nor oath required. For personal study only.

✦ Synopsis

Designed for students of probability and stochastic processes, as well as for students of functional analysis, specifically, this volume presents some chosen parts of functional analysis that can help clarify probability and stochastic processes. The subjects range from basic Hilbert and Banach spaces, through weak topologies and Banach algebras, to the theory of semigroups of bounded linear operators. Numerous standard and non-standard examples and exercises make the book suitable as a course textbook or for self-study.

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## Abstract Let __X~a,b~__ be nonnegative random variables with the property that __X~a,b~ ≦ X~a,c~ + X~c.b~__ for all 0__≦ a < c < b ≦ T__, where __T >__ 0 is fixed. We define __M~a,b~ =__ sup {__X~a,c~: a < c ≦ h__} and establish bounds for __P__[__M~a,b~ ≧ Ξ»__] in terms of given bounds for __P[X