Geodesic
Stochastic Monotonicity and Duality for One-Dimensional Markov Processes
Matematičeskie zametki, Tome 89 (2011) no. 5, pp. 694-704

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The theory of monotonicity and duality is developed for general one-dimensional Feller processes, extending the approach from [1]. Moreover it is shown that local monotonicity conditions (conditions on the Lévy kernel) are sufficient to prove the well-posedness of the corresponding Markov semigroup and process, including unbounded coefficients and processes on the half-line.
Keywords: stochastic monotonicity, duality, one-dimensional Markov process, Lévy–Kchintchine type generator. 
@article{MZM_2011_89_5_a5,
     author = {V. N. Kolokoltsov},
     title = {Stochastic {Monotonicity} and {Duality} for {One-Dimensional} {Markov} {Processes}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {694--704},
     publisher = {mathdoc},
     volume = {89},
     number = {5},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2011_89_5_a5/}
}
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V. N. Kolokoltsov. Stochastic Monotonicity and Duality for One-Dimensional Markov Processes. Matematičeskie zametki, Tome 89 (2011) no. 5, pp. 694-704. http://geodesic.mathdoc.fr/item/MZM_2011_89_5_a5/