Stochastic
- Describes processes driven partly or wholly by randomness.
- Outcomes are not fully determined and can be unpredictable.
- Appears across fields such as mathematics, finance, and physics.
Definition
Section titled “Definition”Stochastic refers to processes that involve randomness or uncertainty. A stochastic process is one in which the outcome is not completely determined and is subject to some degree of randomness.
Explanation
Section titled “Explanation”A stochastic process produces outcomes that cannot be predicted with complete certainty because they are influenced by random factors. These factors may be external influences, inherent variability, or other sources of uncertainty. Because the contributing factors are often difficult to predict with complete accuracy, the behavior of stochastic systems can be unpredictable and require modeling approaches that account for randomness.
Examples
Section titled “Examples”Stock prices
Section titled “Stock prices”The stock market is a classic example of a stochastic process. The price of a particular stock is influenced by a wide range of factors, including economic conditions, company performance, and investor sentiment. These factors are often difficult to predict with complete accuracy, leading to uncertainty about the future price of a stock. As a result, stock prices can be highly unpredictable and subject to significant randomness.
Brownian motion
Section titled “Brownian motion”Brownian motion is a type of random motion that was first observed by botanist Robert Brown in 1827. He noticed that small particles suspended in a liquid seemed to be moving randomly and unpredictably. This motion is now known to be caused by the constant bombardment of the particles by molecules in the liquid. Brownian motion is an example of a stochastic process, as the motion of the particles is not completely determined and is subject to some degree of randomness.
Use cases
Section titled “Use cases”- Present across various fields, including mathematics, finance, and physics.
- Understanding and modeling stochastic processes helps to better understand and predict the behavior of systems subject to randomness and uncertainty.
Notes or pitfalls
Section titled “Notes or pitfalls”- Stochastic systems are inherently unpredictable to some degree because many influencing factors are difficult to predict with complete accuracy.
- Modeling such systems requires accounting for randomness rather than assuming deterministic outcomes.
Related terms
Section titled “Related terms”- Stochastic process
- Brownian motion
- Randomness
- Uncertainty