We prove that any Brownian moving average
Xt=∫−∞t (f(s−t)−f(s)) dBs, t≥0,
satisfies the conditional full support condition introduced by Guasoni, Rásonyi and Schachermayer [Ann. Appl. Probab. 18 (2008) 491–520].
"Brownian moving averages have conditional full support." Ann. Appl. Probab. 18 (5) 1825 - 1830, October 2008. https://doi.org/10.1214/07-AAP502