## The Annals of Probability

### The Range of Stochastic Integration

D. J. H. Garling

#### Abstract

Every measurable real-valued function $f$ on the space of Wiener process paths with $E(|f|^p) < \infty$ (where $0 < p < 1$) can be represented as a stochastic integral $f = \int \varphi dX$, where $E(\int \varphi^2(t)dt)^{p/2} < \infty$. A similar result holds for $1 < p < \infty$ if and only if $E(f) = 0$.

#### Article information

Source
Ann. Probab., Volume 6, Number 2 (1978), 332-334.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176995578

Digital Object Identifier
doi:10.1214/aop/1176995578

Mathematical Reviews number (MathSciNet)
MR471079

Zentralblatt MATH identifier
0387.60065

JSTOR