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In the study of stochastic processes in mathematics, a hitting time (or first hit time) is the first time at which a given process "hits" a given subset of the state space. Exit times and return times are also examples of hitting times. ==Definitions== Let ''T'' be an ordered index set such as the natural numbers, N, the non-negative real numbers, [0, +∞), or a subset of these; elements ''t'' ∈ ''T'' can be thought of as "times". Given a probability space (Ω, Σ, Pr) and a measurable state space ''S'', let ''X'' : Ω × ''T'' → ''S'' be a stochastic process, and let ''A'' be a measurable subset of the state space ''S''. Then the first hit time ''τ''''A'' : Ω → [0, +∞] is the random variable defined by : The first exit time (from ''A'') is defined to be the first hit time for ''S'' \ ''A'', the complement of ''A'' in ''S''. Confusingly, this is also often denoted by ''τ''''A''. The first return time is defined to be the first hit time for the singleton set , which is usually a given deterministic element of the state space, such as the origin of the coordinate system. 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「hitting time」の詳細全文を読む スポンサード リンク
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