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Killed process
In probability theory — specifically, in stochastic analysis — a killed process is a stochastic process that is forced to assume an undefined or "killed" state at some (possibly random) time.
==Definition==
Let ''X'' : ''T'' × Ω → ''S'' be a stochastic process defined for "times" ''t'' in some ordered index set ''T'', on a probability space (Ω, Σ, P), and taking values in a measurable space ''S''. Let ''ζ'' : Ω → ''T'' be a random time, referred to as the killing time. Then the killed process ''Y'' associated to ''X'' is defined by
:
and ''Y''''t'' is left undefined for ''t'' ≥ ''ζ''. Alternatively, one may set ''Y''''t'' = ''c'' for ''t'' ≥ ''ζ'', where ''c'' is a "coffin state" not in ''S''.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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