Transient Probability Functions: A Sample Path Approach
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AC, Discrete Random Walks (DRW'03), DMTCS Proceedings vol. AC, Discrete Random Walks (DRW'03) (2003).

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A new approach is used to determine the transient probability functions of Markov processes. This new solution method is a sample path counting approach and uses dual processes and randomization. The approach is illustrated by determining transient probability functions for a three-state Markov process. This approach also provides a way to calculate transient probability functions for Markov processes which have specific sample path characteristics.
@article{DMTCS_2003_special_248_a29,
     author = {Green, Michael L. and Krinik, Alan and Mortensen, Carrie and Rubino, Gerardo and Swift, Randall J.},
     title = {Transient {Probability} {Functions:} {A} {Sample} {Path} {Approach}},
     journal = {Discrete mathematics & theoretical computer science},
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     volume = {DMTCS Proceedings vol. AC, Discrete Random Walks (DRW'03)},
     year = {2003},
     doi = {10.46298/dmtcs.3349},
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     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3349/}
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Green, Michael L.; Krinik, Alan; Mortensen, Carrie; Rubino, Gerardo; Swift, Randall J. Transient Probability Functions: A Sample Path Approach. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AC, Discrete Random Walks (DRW'03), DMTCS Proceedings vol. AC, Discrete Random Walks (DRW'03) (2003). doi : 10.46298/dmtcs.3349. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3349/

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