Let $W_t$ be the standard Brownian Motion. I am interested on the conditions on $f(\cdot)$ that guarantee that the expectation of the Ito integral below is zero:


Any reference?

ps: it is clear that if $f(\cdot)$ is bounded, it will be zero, but I am pretty sure there must be weaker conditions.


The requirement is simply that $f$ is integrable. An ito integral is approximated by $\sum_{s_i} f(W_{s_i}, s_i) (W_{s_{i+1}} - W_{s_i})$. Since $f(W_{s_i}, s_i)$ is independent of that interval (by definition of brownian motion), the expectation of each summand is zero. The result follows.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.