Maximal inequalities for the Ornstein-Uhlenbeck process
Maximal inequalities for the Ornstein-Uhlenbeck process
Let $V=(V_t)_{t \ge 0}$ be the Ornstein-Uhlenbeck velocity process solving \[ dV_t = - \beta V_t dt + dB_t\] with $V_0=0$ , where $\beta >0$ and $B=(B_t)_{t \ge 0}$ is a standard Brownian motion. Then there exist universal constants $C_1>0$ and $C_2>0$ such that \[ \frac {C_1}{\sqrt { \beta }} …