Increasing process

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An increasing process is a stochastic process

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

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

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

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

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