Discrete vs Continuous Time

Discrete Time

In discrete time systems, the values of variables are given at distinct “points in time”.

For example, in a HASH simulation run the step number is a discrete measure of time within the simulation. Steps are integers (whole numbers), and there are no half-way or in-between steps.

The formal definition of discrete time states that there must be “a positive minimum distance to the nearest other permissible value”.

For example, a time series given in discrete time may increment on an hourly basis, meaning 10:00 and 11:00 may be valid observations, while 10:32:56.83726 would not. Each variable is observed only once per time period.

Continuous Time

On the other hand, in continuous time systems, variables are viewed as potentially having particular values for only infinitesimally short amounts of time. Between any two given points in time or observations there are presumed to be an infinite number of other points.

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Discrete Time
Continuous Time