Brownian moving averages have conditional full support

TL;DR

This paper proves that Brownian moving averages satisfy the conditional full support condition, which has implications for financial modeling and stochastic process theory.

Contribution

It establishes that any Brownian moving average process meets the conditional full support condition, extending previous theoretical results.

Findings

Brownian moving averages satisfy the conditional full support condition

The result applies to a broad class of stochastic processes

Implications for financial mathematics and stochastic analysis

Abstract

We prove that any Brownian moving average \[X_t=\int_{-\infty}^t\bigl(f(s-t)-f(s)\bigr) dB_s,\qquad t\ge0,\] satisfies the conditional full support condition introduced by Guasoni, R\'{a}sonyi and Schachermayer [Ann. Appl. Probab. 18 (2008) 491--520].