Sequences of events take time, so we can think on random events along the time. So, a stochastic process means time and randomness. So, there are factors that make the temperature unpredictable. Below is presented some general concepts of stochastic processes. Stationary increment property means that the probability distribution for the changes in the stochastic variable X, depends only on the time interval length.
Independent increments means that for all time instant t, the increments are independents.
This means that all the past information is considered in the current value, so that futures values of the process depends only on its current value . The futures values are not affected by the past values. It has independent increments . The changes of value over any finite time interval are normally distributed . So, it has stationary increments, besides the property of independent increments.