Increasing process

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An increasing process is a stochastic process...

...where the random variables which make up the process are increasing almost surely and adapted:

A continuous increasing process is such a process where the set is continuous.

Consider a stochastic process satisfying  a.s. for all   My question is: Does there exist a modification of , which almost surely has increasing sample paths ?[1]


  1. ^ "Increasing stochastic process". MathOverflow. Retrieved 2023-05-06.