Seminar on Stochastic Processes, 1986 pp 15-19 | Cite as

# On the Identification of Markov Processes by the Distribution of Hitting Times

## Abstract

J. Glover [6,7] has recently provided a remarkable generalization of the celebrated Blumenthal, Getoor, McKean theorem [2] concerning the identification of Markov processes up to a time change. To state Glover’s theorem let X = (X_{t},P^{x}) and Y = (Y_{t},Q^{x}) be right Markov processes on a common state space (E,*E*). Let Δ ε E be a cemetery point used to render the resolvents of X and Y Markovian. Recall that Δ is a trap for X and for Y; the *lifetime* of X (resp. Y) is then ζ = inf{t: X_{t} = Δ}(resp. n = inf{t: Y_{t} = Δ}). For B ε *E*,let T(B) = inf{t>0: X_{t}εB}, S(B) = inf{t>0: Y_{t}εB}. Recall that X, for example, is *transient* provided its potential kernel U is proper.

## Keywords

Markov Process Time Change Borel Function Identical Cone Finite Dimensional Distribution## Preview

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## References

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