In this note, we study the infinite-dimensional conditional laws of Brownian
semistationary processes. Motivated by the fact that these processes are
typically not semimartingales, we present sufficient conditions ensuring that a
Brownian semistationary process has conditional full support, a property
introduced by Guasoni, R\'asonyi, and Schachermayer [Ann. Appl. Probab., 18
(2008) pp. 491--520]. By the results of Guasoni, R\'asonyi, and Schachermayer,
this property has two important implications. It ensures, firstly, that the
process admits no free lunches under proportional transaction costs, and
secondly, that it can be approximated pathwise (in the sup norm) by
semimartingales that admit equivalent martingale measures.Comment: 7 page
