Geodesic
Characterization of density processes of deformed stochastic bases of the first kind
Informatics and Automation, Stochastic calculus, martingales, and their applications, Tome 287 (2014), pp. 267-278 
I. V. Pavlov; O. V. Nazarko. Characterization of density processes of deformed stochastic bases of the first kind. Informatics and Automation, Stochastic calculus, martingales, and their applications, Tome 287 (2014), pp. 267-278. http://geodesic.mathdoc.fr/item/TRSPY_2014_287_a14/
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     author = {I. V. Pavlov and O. V. Nazarko},
     title = {Characterization of density processes of deformed stochastic bases of the first kind},
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     pages = {267--278},
     year = {2014},
     volume = {287},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2014_287_a14/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We propose a method for reducing a deformed stochastic basis of the first kind to a weakly deformed one. In the case when every $\sigma$-algebra of a filtration is generated by an at most countable partition of the sample space into atoms, we study the problems of constructing deformations of the first kind from a given density process.

[1] Nazarko O.V., Pavlov I.V., “Rekurrentnyi metod postroeniya slabykh deformatsii po protsessu plotnostei v ramkakh modeli stokhasticheskogo bazisa, snabzhennogo spetsialnoi khaarovskoi filtratsiei”, Vestn. Rostov. gos. un-ta putei soobsch., 2012, no. 1, 200–208

[2] Bogachev V.I., Osnovy teorii mery, T. 1, NITs “Regulyarnaya i khaoticheskaya dinamika”, Moskva; Izhevsk, 2006

[3] Pavlov I.V., Nazarko O.V., “Obobschenie teoremy Duba o svobodnom vybore dlya deformirovannykh submartingalov”, UMN., 68:6 (2013), 175–176 | DOI | MR | Zbl

[4] Pavlov I.V., Nazarko O.V., “Teorema o preobrazovanii svobodnogo vybora dlya deformirovannykh submartingalov”, Teoriya veroyatn. i ee primen., 2014 (to appear)

[5] Liptser R.Sh., Shiryaev A.N., Teoriya martingalov, Nauka, M., 1986 | MR | Zbl

[6] Nazarko O.V., “Slabye deformatsii na binarnykh finansovykh rynkakh”, Izv. vuzov. Sev.-Kavk. reg. Estestv. nauki, 2010, no. 1, 12–18 | Zbl