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On the transition from a Markov chain to a continuous time process

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  • Grimvall, Anders

Abstract

Starting from a real-valued Markov chain X0,X1,...,Xn with stationary transition probabilities, a random element {Y(t);t[set membership, variant][0, 1]} of the function space D[0, 1] is constructed by letting Y(k/n)=Xk, k= 0,1,...,n, and assuming Y (t) constant in between. Sample tightness criteria for sequences {Y(t);t[set membership, variant][0,1]};n of such random elements in D[0, 1] are then given in terms of the one-step transition probabilities of the underlying Markov chains. Applications are made to Galton-Watson branching processes.

Suggested Citation

  • Grimvall, Anders, 1973. "On the transition from a Markov chain to a continuous time process," Stochastic Processes and their Applications, Elsevier, vol. 1(4), pages 335-368, October.
    • Handle: RePEc:eee:spapps:v:1:y:1973:i:4:p:335-368
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    Cited by:

    1. Duquesne, Thomas, 2009. "Continuum random trees and branching processes with immigration," Stochastic Processes and their Applications, Elsevier, vol. 119(1), pages 99-129, January.
    2. Duquesne, Thomas & Winkel, Matthias, 2019. "Hereditary tree growth and Lévy forests," Stochastic Processes and their Applications, Elsevier, vol. 129(10), pages 3690-3747.

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