On the dependence between a Wiener process and its running maxima and running minima processes

Karol Dąbrowski, Piotr Jaworski

We study a triple of stochastic processes: a Wiener process $W_t$, $t\ge 0$, its running maxima process $M_t=\sup \{W_s:s\in [0,t]\}$ and its running minima process $m_t=\inf \…