Ramazan Kadiev, Dagestan Research Center of the Russian Academy of Sciences and Department of Mathematics, Dagestan State University, M. Gadgiev st. 43 a, 367025, Makhachkala, Russia, e-mail:kadiev_r@mail.ru;Pyotr Simonov, Perm State National Research University, P. O. Box 7345, 614083, Perm, Russia, e-mail:simpm@mail.ru

**Abstract:** The admissibility of spaces for Itô functional difference equations is investigated by the method of modeling equations. The problem of space admissibility is closely connected with the initial data stability problem of solutions for Itô delay differential equations. For these equations the $p$-stability of initial data solutions is studied as a special case of admissibility of spaces for the corresponding Itô functional difference equation. In most cases, this approach seems to be more constructive and expedient than other traditional approaches. For certain equations sufficient conditions of solution stability are given in terms of parameters of those equations.

**Keywords:** Itô functional difference equation; stability of solutions; admissibility of spaces

**Classification (MSC 2010):** 39A60, 39A30, 60H25, 37H10, 93E15

**DOI:** 10.21136/MB.2016.0059-14

**Full text** available as PDF.

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