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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.

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*.

- Øksendal, Bernt K. (2003).
*Stochastic Differential Equations: An Introduction with Applications*(Sixth ed.). Berlin: Springer. ISBN 3-540-04758-1. (See Section 8.2)