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:TS be a stochastic process defined for "times" t in some ordered index set T, on a probability space (,,P), and taking values in a measurable space S. Let :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. Alternatively, one may set Yt=c for t, where c is a "coffin state" not in S.

See also

• Stopped process

References

• (See Section 8.2)