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

Anders Grimvall

Stochastic Processes and their Applications, 1973, vol. 1, issue 4, 335-368

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.

Keywords: measures; on; function; spaces; Markov; chains; tightness; branching; process (search for similar items in EconPapers)
Date: 1973
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Citations: View citations in EconPapers (2)

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