What are the examples to understand L-process and R-process?

Question

R-processes and L-processes
R-process on $ [0,\infty) $ to signify a process all of whose paths are right-continuous on $[0,\infty)$ with limits from the left on $(0,\infty)$. R-function or R- path on $[0,\infty)$ is defined via the obvious analogous definition. The L-processes on $(0,\infty)$, all of whose paths are left-continuous with limits from the right. How to understnad them in a intutive way

Answer 1

The R- functions are frequently used for probability distribution functions. But if you consider a process, consider for $R$ for example the number of jobs in some factory. It starts with 0 jobs. Then, at some time $t$, a new job arrives. Then, the process makes a jump of size 1 at time $t$. At time $t$, the process has value 1, therefore, the process is not continuous from the left. The function is continuous from the right, since it looks like this (Most real-world processes will be of this type.)

For an $L$-process, you invert the time axis of the above process.