Stochastic Processes – Difference Between Stochastic and Random

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What's the difference between stochastic and random?

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A variable is random. A process is stochastic. Apart from this difference, the two words are synonyms.

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[Math] What’s the difference between open and closed sets

Intuitively speaking, an open set is a set without a border: every element of the set has, in its neighborhood, other elements of the set. If, starting from a point of the open set, you move away a little, you never exit the set.

A closed set is the complement of an open set (i.e. what stays "outside" from the open set).

Note that some set exists, that are neither open nor closed.

[Math] Difference between time series and stochastic process

Basically, a stochastic process is to a time series what a random variable is to a number.

The realization (the "result", the observed value) of a random variable (say, a dice roll) is a number - (but, as it's a random variable, we know that the number can take values from a given set according to some probability law).

The same applies to stochastic process, but now the realization instead of being a single number is a sequence (if the process is discrete) or a function (if it's continuous). Basically, a time series.

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[Math] What’s the difference between open and closed sets

[Math] Difference between time series and stochastic process

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