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Stationary Stochastic Process

A stationary stochastic process is a sequence of random variables that satisfies the property of stationarity.

Definitions:

1. Stationary: In the context of stochastic processes, stationary means that the statistical properties of the process remain constant over time. This property does not depend on absolute time but on the relative positions of observations within the sequence.
2. Stochastic Process: A stochastic process refers to the collection of random variables indexed by time. It is a mathematical model used to describe the evolution of a system over time, where random factors play a significant role.

Examples:

• Example 1: A coin-flipping experiment where the probability of heads or tails remains the same regardless of when the flip occurs, is a stationary stochastic process.
• Example 2: The daily stock prices of a company, assuming that the statistical properties of the process remain constant, can be modeled as a stationary stochastic process.

Possible Related Products:

To learn more about the concepts of stationary stochastic processes, you may find the following books helpful:

• Stationary Stochastic Processes by Georg Lindgren
• Stochastic Processes by Sheldon M. Ross
• Probability Theory: A Concise Course by Y.A. Rozanov