Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I need to calculate the expectation of the product between the integral of a Wiener process and the expectation of a Wiener process. Is the same as the expectation of the product between the integral and comprehensive Wiener by Wiener $t$. The integrals are evaluated between $0$ and $1$.

Necesito calcular la expectativa del producto entre la integral de un proceso de Wiener y la expectativa de un proceso de Wiener. Lo que es lo mismo la expectativa del producto entre la integral de Wiener y la integral de $t$ por Wiener. las integrales se evaluan entre $0$ y $1$.

share|cite|improve this question

Hint: For every $s$ and $t$, $\mathbb E(W(s)W(t))=\min(s,t)$. Apply this to $$ \mathbb E\left(\int_0^1W(s)\mathrm ds\cdot\int_0^1t\,W(t)\mathrm dt\right)=\int_0^1\!\!\!\int_0^1t\cdot\mathbb E\left(W(s)W(t)\right)\mathrm dt\mathrm ds.$$

share|cite|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

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