This has the following consequence: Proposition 8 For any random variable X, liin,1nOO,(E[|XlT])1/'" : llXllOO' Proof If |\X\|Oo : O,X : O a.e., the result is true. So let O < /4: = \|X|\Oo ยง oo. Then, by definition, P[|X| > k] : O.
The book is a completely revised and enlarged version of the author's Stochastic Processes and Integration (Noordhoff, 1979). The new title reflects the content and generality of the extensive amount of new material.
... Vector Measures, Amer. Math. Soc. Surveys, Providence, RI, 1977. Dinculeanu, N. [1] Vector Measures, Pergamon Press, London, UK, 1967. [2] Vector Integration and Stochastic Integration in Banach Spaces, Wiley-Interscience, New York ...
Stochastic Processes: General Theory starts with the fundamental existence theorem of Kolmogorov, together with several of its extensions to stochastic processes. It treats the function theoretical aspects of processes and...
This is a revised and expanded edition of a successful graduate and reference text. The book is designed for a standard graduate course on probability theory, including some important applications.