On the path structure of a semimartingale arising from monotone probability theory

Alexander C. R. Belton

Let $X$ be the unique normal martingale such that $X_0=0$ and \[\mathrm{d}[X]_t=(1-t-X_{t-}) \mathrm{d}X_t+\mathrm{d}t\] and let $Y_t:=X_t+t$ for all $t\ge 0$; the semimartingale…