Abstract
We study the paths of general random evolution processes obtained by piecing together deterministic evolution functions according to the dictates of a regular step process. If the state space is metrizable we show that such processes are strong Markov; and they are even standard under a certain continuity condition on paths. We apply this result to solutions of stochastic delayed differential equations, and we make a connection between our processes and random evolutions associated with classes of semigroups.
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Research supported in part by National Science Foundation grant GP 28658.
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Erickson, R.V. Paths of random evolutions. Z. Wahrscheinlichkeitstheorie verw Gebiete 29, 309–321 (1974). https://doi.org/10.1007/BF00532715
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DOI: https://doi.org/10.1007/BF00532715