Geodesic
On equivalence of predictable and natural stochastic processes
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 3 (2018), pp. 58-71

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A new approach to study of predictable stochastic processes is suggested. This approach is based on the Doob proof of the Doleans-Dad theorem about equivalence of increasing predictable and natural stochastic processes. A generalization of the Doob theorem about uniform approximation of an indicator function is proved. With the help of this degeralization it is proved that the Doleans-Dad theorem is valid fot stochastic processes with integrable variation.
Keywords: markov moments (stopping times), natural processes, predictable stochastic processes. 
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     author = {V. M. Kruglov},
     title = {On equivalence of predictable and natural stochastic processes},
     journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
     pages = {58--71},
     publisher = {mathdoc},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTPMK_2018_3_a3/}
}
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V. M. Kruglov. On equivalence of predictable and natural stochastic processes. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 3 (2018), pp. 58-71. http://geodesic.mathdoc.fr/item/VTPMK_2018_3_a3/