Geodesic
Construction of Non-Homogeneous Markov Processes by Means of a Random Substitution of Time
Teoriâ veroâtnostej i ee primeneniâ, Tome 6 (1961) no. 1, pp. 47-56

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It is proved that a continuous single-dimensional Markov process $y(t)$ with wide restrictions can be obtained from the Wiener process $x(t)$ in the following form: $y(t)=\psi[x(\tau_t),t]$, where $\psi(x,t)$ is a continuous function, monotonic in $x$ for a given $t$, and $\tau _t $ is a non-decreasing random function of $t$ (Theorem 1). Conditions are given which should be met by the Markov process $x(t)$ in abstract space and the random function $\tau_t$ so that the process $y(t)=x(\tau_t)$ will also be a Markov process (Theorem 2). 
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     author = {V. A. Volkonskii},
     title = {Construction of {Non-Homogeneous} {Markov} {Processes} by {Means} of a {Random} {Substitution} of {Time}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {47--56},
     publisher = {mathdoc},
     volume = {6},
     number = {1},
     year = {1961},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1961_6_1_a2/}
}
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V. A. Volkonskii. Construction of Non-Homogeneous Markov Processes by Means of a Random Substitution of Time. Teoriâ veroâtnostej i ee primeneniâ, Tome 6 (1961) no. 1, pp. 47-56. http://geodesic.mathdoc.fr/item/TVP_1961_6_1_a2/