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
- 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
- $1$: Introduction:
- 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
- $2.1$ Autocorrelation Properties of Stationary Models:
- $2$: Autocorrelation Function and Spectrum of Stationary Processes:
- Part $\text {I}$: Stochastic Models and their Forecasting:
- 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