Increasing process

where the random variables ${\displaystyle X_{t}}$ which make up the process are increasing almost surely and adapted:

${\displaystyle 0=X_{0}\leq X_{t_{1}}\leq \cdots .}$

An increasing process is a stochastic process

${\displaystyle (X_{t})_{t\in M}}$

A continuous increasing process is such a process where the set ${\displaystyle M}$ is continuous.