O'Reilly logo

Stochastic Finance, 4th Edition by Alexander Schied, Hans Föllmer

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

A.7 Some functional analysis

Numerous arguments in this book involve infinite-dimensional vector spaces. Typical examples arising in connection with a probability space (Ω,F, P) are the spaces Lp := Lp(Ω,F, P) for 0 p , which we will introduce below. To this end, we first take p (0,] and denote by Lp(Ω,F, P) the set of all F-measurable functions Z on (Ω,F, P) such that Zp < , where

Let us also introduce the space L0(Ω,F, P), defined as the set of all P-a.s. finite random variables. If no ambiguity with respect to σ-algebra and measure can arise, we may sometimes write Lp(P) or just Lp instead of Lp(Ω,F, P). For p [0,], the space

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