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In mathematics, the law of a stochastic process is the measure that the process induces on the collection of functions from the index set into the state space. The law encodes a lot of information about the process; in the case of a random walk, for example, the law is the probability distribution of the possible trajectories of the walk. ==Definition== Let (Ω, ''F'', P) be a probability space, ''T'' some index set, and (''S'', Σ) a measurable space. Let ''X'' : ''T'' × Ω → ''S'' be a stochastic process (so the map : is a (''F'', Σ)-measurable function for each ''t'' ∈ ''T''). Let ''S''''T'' denote the collection of all functions from ''T'' into ''S''. The process ''X'' (by way of currying) induces a function Φ''X'' : Ω → ''S''''T'', where : The law of the process ''X'' is then defined to be the pushforward measure : on ''S''''T''. 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「Law (stochastic processes)」の詳細全文を読む スポンサード リンク
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