O'Reilly logo

Asymptotic Statistics by A.W. van der Vaart

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

18

Stochastic Convergence in Metric Spaces

           This chapter extends the concepts of convergence in distribution, in probability, and almost surely from Euclidean spaces to more abstract metric spaces. We are particularly interested in developing the theory for random functions, or stochastic processes, viewed as elements of the metric space of all bounded functions.

18.1 Metric and Normed Spaces

In this section we recall some basic topological concepts and introduce a number of examples of metric spaces.

    A metric space is a set image equipped with a metric. A metric or distance function is a map with the properties

       (i)  d(x, y) = ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required