Initial data stability and admissibility of spaces for Itô linear difference equations. (English) Zbl 1463.39043

Summary: 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.


39A50 Stochastic difference equations
39A30 Stability theory for difference equations
37H10 Generation, random and stochastic difference and differential equations
Full Text: DOI