Continuous One-Dimensional Markov Processes and Additive Functionals Derived from Them
Teoriâ veroâtnostej i ee primeneniâ, Tome 4 (1959) no. 2, pp. 208-211
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The terminology and symbols employed are the same as in [1] and [2]. The paper describes all continuous Feller one-dimensional Markov processes, which are regular within a segment and gives their infinitesimal operators (Theorem 4). It is stated that each such process is a sub-process of a non-terminating process of the same type (Theorems and 1'). Therefore, a description of all processes amounts to a description of all multiplicative or additive functionals corresponding to regular Feller sub-processes of non-terminating processes.
@article{TVP_1959_4_2_a5,
author = {V. A. Volkonskii},
title = {Continuous {One-Dimensional} {Markov} {Processes} and {Additive} {Functionals} {Derived} from {Them}},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {208--211},
year = {1959},
volume = {4},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1959_4_2_a5/}
}
V. A. Volkonskii. Continuous One-Dimensional Markov Processes and Additive Functionals Derived from Them. Teoriâ veroâtnostej i ee primeneniâ, Tome 4 (1959) no. 2, pp. 208-211. http://geodesic.mathdoc.fr/item/TVP_1959_4_2_a5/