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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.〔 M. Kac & J. Logan, in ''Fluctuation Phenomena'', eds. E.W. Montroll & J.L. Lebowitz, North-Holland, Amsterdam, 1976 〕〔 E. Nelson, ''Quantum Fluctuations'', Princeton University Press, Princeton, 1985 〕 Stochastic systems and processes play a fundamental role in mathematical models of phenomena in many fields of science, engineering, finance and economics. ==Mathematical theory== The use of the term ''stochastic'' to mean ''based on the theory of probability'' goes back to a 1917 publication by Ladislaus Bortkiewicz (1868–1931).〔''The Oxford English Dictionary'' s.v. "stochastic" quotes: "Die an der Wahrscheinlichkeitstheorie orientierte, somit auf ‘das Gesetz der Grossen Zahlen’ sich gründende Betrachtung empirischer Vielheiten möge als Stochastik..bezeichnet werden." - 1917 L. von Bortkiewicz: ''Die Iterationen'' 3〕 Bortkiewicz used it in the sense of ''making conjectures'' that the Greek term has borne since the days of the ancient philosophers, and after the title of ''Ars Conjectandi'' that Jakob Bernoulli gave to his work (published in 1713) on probability theory. In mathematics, specifically in probability theory, the field of stochastic processes has been a major area of research. As an extension of mathematical theories, stochastic game theory is another application of these principles. A stochastic matrix is a matrix that has non-negative real entries that sum to one in each column, row, or both. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Stochastic」の詳細全文を読む スポンサード リンク
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