## ::Stochastic

### ::concepts

Theory::monte Carlo::process Music::which Science::random System::systems Language::methods

{{#invoke:Hatnote|hatnote}}
The term * stochastic* occurs in a wide variety of professional or academic fields to describe events or systems that are unpredictable due to the influence of a random variable. The word "stochastic" comes from the Greek word στόχος (

*stokhos*, "aim").

Researchers refer to physical systems in which they are uncertain about the values of parameters, measurements, expected input and disturbances as "stochastic systems". In probability theory, a purely stochastic system is one whose state is randomly determined, having a random probability distribution or pattern that may be analyzed statistically but may not be predicted precisely. In this regard, it can be classified as non-deterministic (i.e., "random") so that the subsequent state of the system is determined probabilistically. Any system or process that must be analyzed using probability theory is stochastic at least in part.<ref>
M. Kac & J. Logan, in *Fluctuation Phenomena*, eds. E.W. Montroll & J.L. Lebowitz, North-Holland, Amsterdam, 1976
</ref><ref>
E. Nelson, *Quantum Fluctuations*, Princeton University Press, Princeton, 1985
</ref>
Stochastic systems and processes play a fundamental role in mathematical models of phenomena in many fields of science, engineering, finance and economics.

**Stochastic sections**

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