Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Suppose $W_t$ is a standard one dimensional Brownian motion. Let $M_t$ and $I_t$ be its running maximum and time integral, respectively:

    $$M_t=\max_{0\leq s\leq t}\,W_s$$

The laws of $M_t$ and $I_t$ can be easily derived by any beginnner studying stochastic processes. However, I haven't seen anything in the literature about their joint law. Is the joint law of $M_t$ and $I_t$ known?

share|improve this question

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.