Definition:Stochastic Process

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Definition

A stochastic process is a collection of random variables defined on a probability space indexed by a subset of the real numbers, $T \subseteq \mathbb{R}$. In the most well studied settings, $T \subseteq \mathbb{Z}$ and time series are realizations of the stochastic process.


Also known as

A stochastic process is also known as a random process.


Also see

  • Results about stochastic processes can be found here.


Sources

$1$: Introduction:
$1.2$ Stochastic and Deterministic Dynamic Mathematical Models
Part $\text {I}$: Stochastic Models and their Forecasting:
$2$: Autocorrelation Function and Spectrum of Stationary Processes:
$2.1$ Autocorrelation Properties of Stationary Models:
$2.1.1$ Time Series and Stochastic Processes: Deterministic and statistical time series