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

My continuous-time, continuous step Stochastic Process P runs from time $t=0$ to $t=t_f$ and generates a path. I am able to observe its starting and ending position (so $P(0)=a$ and $P(t_f)=b$), but I'm unsure what happened in the middle. I want to come up with a PDF for the integral of the process from $0$ to $t_f$.

Any advice?

share|cite|improve this question
There isn't enough information to find the pdf. – Sasha May 4 '12 at 0:40
There isn't? Really? $P$ is known: I have at my disposal a PDF for the location of the process at any time $t$. I can't think of what more information would be needed. – gmb May 4 '12 at 0:53
I suggest you improve your question to make it explicit what is known. For example, $P$ might be defined in terms of SDE, but the expression for pdf of $P(t)$ might not be available. In order to find pdf of $P(t)$, you need to find the joint pdf for $(P(t), P(t_f))$ and then condition on $P(t_f)=b$. – Sasha May 4 '12 at 0:59

If I'm not mistaken, if you have a SDE for your process under Ito form, there is under conditions a way to go to the forward and backward equations which gives the time evolution of the probability density. Is it helpful ?

share|cite|improve this answer

Your Answer


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.