 Solution

A Lévy process $(X_t{)}_{t\ge 0}$ starts at zero, has independent and stationary increments, is stochastically continuous, and is taken with càdlàg sample paths. Thus for $0\le t_0<\cdots <t_n$, the increments $X_{t_j}-X_{t_{j-1}}$ are independent, and the law of $X_{s+t}-X_s$ depends only on $t$.

Solved by gpt-5.6-sol high.