MathOverflow is a question and answer site for professional mathematicians. 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

The Skorokhod Embedding Problem is well known and has many documented solutions in the literature.

Now if we are given a Brownian stochastic basis (satisfying usual hypothesis), a diffusion $X_t$ (with explicit SDE or transition semigroup, or infinitesimal generator), and a stopping time $\tau$ (let's say a.s. finite).

I was wondering if (or when) it was possible to find a process $Y_t$ such that $Y_1=X_{\tau}$ and where the dynamics of $Y_t$ is explicitely know (aka an exlicit SDE for $Y$, or its transition semigroup).

Best Regards

share|cite|improve this question
The question as it is asked is really general so do not hesitate to give particular cases where a solution is attainable. – The Bridge Mar 1 '11 at 9:48
May be this could do the (theoretical) trick, define $\mathcal{G_t}=\mathcal{F}_t\vee \tau$ the augmented filtration of the original stocahstic basis, then defining $Y_t=E[X_\tau| \mathcal{G}_t]$ would be correct answer. anyway this is still theoretical since this doesn't give analytical form to the $Y$ process – The Bridge Mar 1 '11 at 14:57

Your Answer


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

Browse other questions tagged or ask your own question.