Definition:Stochastic Process

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

• 1965: D.R. Cox and H.D. Miller: The Theory of Stochastic Processes ... (next): Preface

• 1994: George E.P. Box, Gwilym M. Jenkins and Gregory C. Reinsel: Time Series Analysis: Forecasting and Control (3rd ed.) ... (previous) ... (next):

$1$: Introduction:

$1.2$ Stochastic and Deterministic Dynamic Mathematical Models

• 1994: George E.P. Box, Gwilym M. Jenkins and Gregory C. Reinsel: Time Series Analysis: Forecasting and Control (3rd ed.) ... (previous) ... (next): Part $\text {I}$: Stochastic Models and their Forecasting

• 1994: George E.P. Box, Gwilym M. Jenkins and Gregory C. Reinsel: Time Series Analysis: Forecasting and Control (3rd ed.) ... (previous) ... (next):

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

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Entry: stochastic process
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Entry: stochastic process