词条 | Killed process |
释义 |
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. DefinitionLet 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 Yt is left undefined for t ≥ ζ. Alternatively, one may set Yt = c for t ≥ ζ, where c is a "coffin state" not in S. See also
References
| last = Øksendal | first = Bernt K. | authorlink = Bernt Øksendal | title = Stochastic Differential Equations: An Introduction with Applications | edition = Sixth | publisher=Springer | location = Berlin | year = 2003 | isbn = 3-540-04758-1 }} (See Section 8.2) 1 : Stochastic processes |
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